novaBBS - sci.math - Re: Natural numbers and vases III

Re: Natural numbers and vases III

<3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>

https://www.novabbs.com/tech/article-flat.php?id=109210&group=sci.math#109210

X-Received: by 2002:a05:622a:1350:b0:31f:1cb2:926d with SMTP id w16-20020a05622a135000b0031f1cb2926dmr15354670qtk.279.1660586610125;
Mon, 15 Aug 2022 11:03:30 -0700 (PDT)
X-Received: by 2002:a05:6870:8890:b0:101:db34:3ed6 with SMTP id
m16-20020a056870889000b00101db343ed6mr11959914oam.151.1660586609836; Mon, 15
Aug 2022 11:03:29 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.misty.com!border-2.nntp.ord.giganews.com!nntp.giganews.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Mon, 15 Aug 2022 11:03:29 -0700 (PDT)
In-Reply-To: <47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7744:c7e6:352d:da10:c656:4f48;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7744:c7e6:352d:da10:c656:4f48
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 15 Aug 2022 18:03:30 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 28

by: WM - Mon, 15 Aug 2022 18:03 UTC

Re: Natural numbers and vases III

<tde2dk$cjc$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109212&group=sci.math#109212

copy link Newsgroups: sci.math

Path: i2pn2.org!rocksolid2!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 13:14:09 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tde2dk$cjc$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com>
<8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com>
<abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com>
<fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com>
<f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com>
<0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com>
<7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com>
<tdd1lo$3iac1$1@dont-email.me>
<ead79949-6c49-4574-ba77-e53dab6ae749n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="12908"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US

by: Sergio - Mon, 15 Aug 2022 18:14 UTC

On 8/15/2022 12:58 PM, WM wrote:
> FromTheRafters schrieb am Montag, 15. August 2022 um 10:55:30 UTC+2:
>> After serious thinking WM wrote :
>>> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
>>>> On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
>>>>> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
>>>>>> On Thursday, August 11, 2022 at 3:00:07 PM UTC+2, WM wrote:
>>>>>>
>>>>>>> Very correct! All must happen element by element, i.e., as steps of a
>>>>>>> super task.
>>>>>>
>>>>>> Du hast einen Riesensprung in der Schüssel.
>>>>>>
>>>>>> Please elaborate how this could be done for uncountable sets. (Say, [-1,
>>>>>> 1] and IR.)
>>>>>>
>>>>>> See: https://en.wikipedia.org/wiki/Uncountable_set
>>>> NO ANSWER? WHY NOT?!
>>>
>>> 1) there are no uncountable sets.
>> Have you 'thrown out' the powerset axiom?
>
> For definable elements of sets yes. Simplest proof is the Binary Tree. In order to distinguish n Objects, you need at least n properties. For distinguishing n paths you need at least n properties. For n paths distinguishable by nodes you need n nodes. And if paths are not distinguishable by nodes then also Cantor's diagonal is not definable by digits.

Your stew pot was left way too long on the burner.

Your nodes have all slipped off your cracker.

Your above sentence with the meaningful words removed, note how you swing from one bs term to the other bs term;

"definable distinguish distinguishing distinguishable distinguishable definable"

>
> Regards, WM

Re: Natural numbers and vases III

<tde3lo$tul$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109219&group=sci.math#109219

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 13:35:33 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tde3lo$tul$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com>
<210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com>
<a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com>
<dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com>
<c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com>
<39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com>
<7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com>
<b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
<3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="30677"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Mon, 15 Aug 2022 18:35 UTC

Re: Natural numbers and vases III

<tde3tq$3ock6$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109220&group=sci.math#109220

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 14:39:51 -0400
Organization: Peripheral Visions
Lines: 27
Message-ID: <tde3tq$3ock6$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com> <6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com> <25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com> <d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com> <615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com> <f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com> <6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com> <34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <tdd1lo$3iac1$1@dont-email.me> <ead79949-6c49-4574-ba77-e53dab6ae749n@googlegroups.com>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 15 Aug 2022 18:39:54 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="e4fc4cde420b0332d5e605cb5a80da80";
logging-data="3945094"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18r9J8caYIXomLGpj9jHFcTM4nRb7Xfhmg="
Cancel-Lock: sha1:iyL9dqxBcIv/PcthIFsetcfdXvQ=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Mon, 15 Aug 2022 18:39 UTC

Re: Natural numbers and vases III

<tde40t$3odia$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109222&group=sci.math#109222

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 14:41:30 -0400
Organization: Peripheral Visions
Lines: 27
Message-ID: <tde40t$3odia$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com> <89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com> <4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com> <21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com> <d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com> <16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com> <d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com> <2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com> <47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 15 Aug 2022 18:41:33 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="e4fc4cde420b0332d5e605cb5a80da80";
logging-data="3946058"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX185eCo+zseCVMjHv1ozVbkKXaNNP893Wm0="
Cancel-Lock: sha1:gGy6JZqa2+zskVmZMvYrt7qS0pc=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb

by: FromTheRafters - Mon, 15 Aug 2022 18:41 UTC

Re: Natural numbers and vases III

<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109224&group=sci.math#109224

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:d02:b0:474:81cc:599e with SMTP id 2-20020a0562140d0200b0047481cc599emr14818184qvh.29.1660589623938;
Mon, 15 Aug 2022 11:53:43 -0700 (PDT)
X-Received: by 2002:a05:6808:30a0:b0:343:5e60:b1f3 with SMTP id
bl32-20020a05680830a000b003435e60b1f3mr7041804oib.242.1660589623681; Mon, 15
Aug 2022 11:53:43 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Mon, 15 Aug 2022 11:53:43 -0700 (PDT)
In-Reply-To: <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Mon, 15 Aug 2022 18:53:43 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 9054

by: William - Mon, 15 Aug 2022 18:53 UTC

Re: Natural numbers and vases III

<aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109225&group=sci.math#109225

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:dac:b0:476:afa0:4191 with SMTP id h12-20020a0562140dac00b00476afa04191mr14461977qvh.36.1660590587646;
Mon, 15 Aug 2022 12:09:47 -0700 (PDT)
X-Received: by 2002:a05:6870:14d0:b0:10e:5961:a12f with SMTP id
l16-20020a05687014d000b0010e5961a12fmr11207233oab.298.1660590587379; Mon, 15
Aug 2022 12:09:47 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Mon, 15 Aug 2022 12:09:47 -0700 (PDT)
In-Reply-To: <19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7744:c7e6:352d:da10:c656:4f48;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7744:c7e6:352d:da10:c656:4f48
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 15 Aug 2022 19:09:47 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 9927

by: WM - Mon, 15 Aug 2022 19:09 UTC

William schrieb am Montag, 15. August 2022 um 20:53:48 UTC+2:
> On Monday, August 15, 2022 at 3:03:33 PM UTC-3, WM wrote:
> > William schrieb am Sonntag, 14. August 2022 um 21:51:38 UTC+2:
> > > On Sunday, August 14, 2022 at 1:50:12 PM UTC-3, WM wrote:
> > >
> > > > The Peano-"set" is not a set
> > > Piffle
> > > >but a potentially infinite collection. This is proved by
> > > > ∀n ∈ ℕ[]: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> > > >
> > > > But there are not two consecutive sets of card ℵo before ω.
> > > Corect
> > >
> > > >So all n which belong to [a] Peano [set[ and have ℵo successors
> > >
> > > "all n which belong to a Peano set and have ℵo successors" is one set. There is no second set.
> > The successors do not vanish. They follow beyond every Peano number.
> So what? Beyond each Peano number are only more elements of the single set "all n which belong to a Peano set and have ℵo successors". There are no successors which do not belong to this set.

Then the successors could be exhausted.
They cannot be exhausted by individual subtraction:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
But they can be exhausted by collective subtraction such that nothing remains.
ℕ \ ℕ 0 { }.'
This is a difference.

> > > "all n which belong to a Peano set and have ℵo successors " has cardinality ℵo.
> > Impossible. There are ℵo successors following each and every Peano number.

But most successors are not Peano numbers. Otherwise they could all be removed such that no successors remained.

> Indeed, there are ℵo successors to every *element* of the set "all n which belong to a Peano set and have ℵo successors"

Subtract all. Then you can say: I have subtracted all Peano numbers but most Peano numbers remain as successors. Contradiction. All means all without remainder.

> However the *set* "all n which belong to a Peano set and have ℵo successors" is not followed by anything.

The reason of this difference is clearly dark numbers.

Regards, WM

Re: Natural numbers and vases III

<337c1fe2-aade-4f62-bee4-e2d58f8293b5n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109227&group=sci.math#109227

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4245:b0:6b9:9b7:11d with SMTP id w5-20020a05620a424500b006b909b7011dmr12396150qko.579.1660592842917;
Mon, 15 Aug 2022 12:47:22 -0700 (PDT)
X-Received: by 2002:a05:6808:df1:b0:344:5db2:e25a with SMTP id
g49-20020a0568080df100b003445db2e25amr4955405oic.1.1660592842708; Mon, 15 Aug
2022 12:47:22 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Mon, 15 Aug 2022 12:47:22 -0700 (PDT)
In-Reply-To: <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=134.190.131.2; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 134.190.131.2
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <337c1fe2-aade-4f62-bee4-e2d58f8293b5n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Mon, 15 Aug 2022 19:47:22 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8263

by: Gus Gassmann - Mon, 15 Aug 2022 19:47 UTC

Re: Natural numbers and vases III

<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109228&group=sci.math#109228

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:507:b0:344:6fcf:78f6 with SMTP id l7-20020a05622a050700b003446fcf78f6mr226490qtx.415.1660593718875;
Mon, 15 Aug 2022 13:01:58 -0700 (PDT)
X-Received: by 2002:a54:448a:0:b0:344:99d1:1578 with SMTP id
v10-20020a54448a000000b0034499d11578mr3132264oiv.7.1660593718664; Mon, 15 Aug
2022 13:01:58 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Mon, 15 Aug 2022 13:01:58 -0700 (PDT)
In-Reply-To: <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Mon, 15 Aug 2022 20:01:58 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 8062

by: William - Mon, 15 Aug 2022 20:01 UTC

Re: Natural numbers and vases III

<tdet6m$1stu$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109248&group=sci.math#109248

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 20:51:17 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tdet6m$1stu$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com>
<a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com>
<dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com>
<c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com>
<39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com>
<7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com>
<b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
<3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>
<aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="62398"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Tue, 16 Aug 2022 01:51 UTC

On 8/15/2022 2:09 PM, WM wrote:
> William schrieb am Montag, 15. August 2022 um 20:53:48 UTC+2:
>> On Monday, August 15, 2022 at 3:03:33 PM UTC-3, WM wrote:
>>> William schrieb am Sonntag, 14. August 2022 um 21:51:38 UTC+2:
>>>> On Sunday, August 14, 2022 at 1:50:12 PM UTC-3, WM wrote:
>>>>
>>>>> The Peano-"set" is not a set
>>>> Piffle
>>>>> but a potentially infinite collection. This is proved by
>>>>> ∀n ∈ ℕ[]: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>>>
>>>>> But there are not two consecutive sets of card ℵo before ω.
>>>> Corect
>>>>
>>>>> So all n which belong to [a] Peano [set[ and have ℵo successors
>>>>
>>>> "all n which belong to a Peano set and have ℵo successors" is one set. There is no second set.
>>> The successors do not vanish. They follow beyond every Peano number.
>> So what? Beyond each Peano number are only more elements of the single set "all n which belong to a Peano set and have ℵo successors". There are no successors which do not belong to this set.
>
> Then the successors could be exhausted.
> They cannot be exhausted by individual subtraction:
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

that equation does not "exhaust" a set at all. It does not "do" anything.

It simply says the Endsegment(n+1) is infinite. (because you stopped at n)

> But they can be exhausted by collective subtraction such that nothing remains.
> ℕ \ ℕ 0 { }.'

trivial.

> This is a difference.
>
>>>> "all n which belong to a Peano set and have ℵo successors " has cardinality ℵo.
>>> Impossible. There are ℵo successors following each and every Peano number.
>

>
> The reason of this difference is clearly dark numbers.

wrong. The reason is that your set of synapses has been exhausted, they are losing identity and becoming dark, without remainders, and no successors.

>
> Regards, WM

Re: Natural numbers and vases III

<d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109258&group=sci.math#109258

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5ccf:0:b0:474:7201:6789 with SMTP id iu15-20020ad45ccf000000b0047472016789mr16666083qvb.75.1660634707148;
Tue, 16 Aug 2022 00:25:07 -0700 (PDT)
X-Received: by 2002:a4a:e7c4:0:b0:445:180:3f87 with SMTP id
y4-20020a4ae7c4000000b0044501803f87mr5961608oov.0.1660634706907; Tue, 16 Aug
2022 00:25:06 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 00:25:06 -0700 (PDT)
In-Reply-To: <be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=185.219.140.163; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 185.219.140.163
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com>
<be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Tue, 16 Aug 2022 07:25:07 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8904

by: zelos...@gmail.com - Tue, 16 Aug 2022 07:25 UTC

måndag 15 augusti 2022 kl. 17:50:23 UTC+2 skrev WM:
> Fritz Feldhase schrieb am Montag, 15. August 2022 um 03:59:25 UTC+2:
> > On Friday, August 12, 2022 at 3:01:07 PM UTC+2, WM wrote:
>
> > > 1) there are no uncountable sets.
> > In set theory they are. Especially in Cantor's "transfinite set theory"..
> No, they are not existing.

Except they are, aleph_0 is countable, aleph_1 is not

> > > 2) They can be counted too. Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]
>
> >
> > Ah, I see: they don't exist. But they can be counted too.
> According to Cantor!

Cantor never said uncountable ones can be counted, he explicitly proved they can't and |P(S)|>|S|

> > Hint: It's clear that Cantor DID NOT talk about a "stepwise process" here:
> >
> > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]
> Element für Element = Schritt für Schritt.

Does not mean what you want it to

> >
> > Actually, he didn't talk about a process here at all.
> He did: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand".
> >
> > > Element für Element defined a process.
> >
> > Could please describe a stepwise process that relates all elements in [-1, 1] to all elements in IR (in a one-to-one fashon)?
> I do not claim that possible.

Which is why mathematics don't do step processes!

>
> Regards, WM

Re: Natural numbers and vases III

<41c165e3-c90b-46ca-a104-568de9a19b3fn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109259&group=sci.math#109259

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:2aa6:b0:474:844b:24ff with SMTP id js6-20020a0562142aa600b00474844b24ffmr17346020qvb.51.1660635413541;
Tue, 16 Aug 2022 00:36:53 -0700 (PDT)
X-Received: by 2002:a05:6830:6613:b0:61c:acf8:8e41 with SMTP id
cp19-20020a056830661300b0061cacf88e41mr6853263otb.298.1660635413277; Tue, 16
Aug 2022 00:36:53 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 00:36:53 -0700 (PDT)
In-Reply-To: <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=185.219.140.163; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 185.219.140.163
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <41c165e3-c90b-46ca-a104-568de9a19b3fn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Tue, 16 Aug 2022 07:36:53 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 10395

by: zelos...@gmail.com - Tue, 16 Aug 2022 07:36 UTC

måndag 15 augusti 2022 kl. 21:09:52 UTC+2 skrev WM:
> William schrieb am Montag, 15. August 2022 um 20:53:48 UTC+2:
> > On Monday, August 15, 2022 at 3:03:33 PM UTC-3, WM wrote:
> > > William schrieb am Sonntag, 14. August 2022 um 21:51:38 UTC+2:
> > > > On Sunday, August 14, 2022 at 1:50:12 PM UTC-3, WM wrote:
> > > >
> > > > > The Peano-"set" is not a set
> > > > Piffle
> > > > >but a potentially infinite collection. This is proved by
> > > > > ∀n ∈ ℕ[]: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> > > > >
> > > > > But there are not two consecutive sets of card ℵo before ω.
> > > > Corect
> > > >
> > > > >So all n which belong to [a] Peano [set[ and have ℵo successors
> > > >
> > > > "all n which belong to a Peano set and have ℵo successors" is one set. There is no second set.
> > > The successors do not vanish. They follow beyond every Peano number.
> > So what? Beyond each Peano number are only more elements of the single set "all n which belong to a Peano set and have ℵo successors". There are no successors which do not belong to this set.
> Then the successors could be exhausted.

Nothing is exhausted, every natural number has a successor

> They cannot be exhausted by individual subtraction:

Meaningless

> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

remove the _def and it is still fuckign true because your __defi s meaningless.

> But they can be exhausted by collective subtraction such that nothing remains.
> ℕ \ ℕ 0 { }.'
> This is a difference.

The difference is you are using first a finite set then the set itself. Nothing else.

> > > > "all n which belong to a Peano set and have ℵo successors " has cardinality ℵo.
> > > Impossible. There are ℵo successors following each and every Peano number.
> But most successors are not Peano numbers. Otherwise they could all be removed such that no successors remained.

False, all successors are.

> > Indeed, there are ℵo successors to every *element* of the set "all n which belong to a Peano set and have ℵo successors"
> Subtract all. Then you can say: I have subtracted all Peano numbers but most Peano numbers remain as successors. Contradiction. All means all without remainder.
> > However the *set* "all n which belong to a Peano set and have ℵo successors" is not followed by anything.
> The reason of this difference is clearly dark numbers.

False

>
> Regards, WM

Re: Natural numbers and vases III

<232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109268&group=sci.math#109268

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:6b18:0:b0:343:6b3:60ff with SMTP id w24-20020ac86b18000000b0034306b360ffmr17714569qts.176.1660644626680;
Tue, 16 Aug 2022 03:10:26 -0700 (PDT)
X-Received: by 2002:aca:5d41:0:b0:342:ac18:e523 with SMTP id
r62-20020aca5d41000000b00342ac18e523mr11826904oib.130.1660644626254; Tue, 16
Aug 2022 03:10:26 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 03:10:26 -0700 (PDT)
In-Reply-To: <814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7744:c77e:1892:c183:a65f:8f2c;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7744:c77e:1892:c183:a65f:8f2c
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 16 Aug 2022 10:10:26 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 8587

by: WM - Tue, 16 Aug 2022 10:10 UTC

Re: Natural numbers and vases III

<169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109269&group=sci.math#109269

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:13ca:b0:343:129:8894 with SMTP id p10-20020a05622a13ca00b0034301298894mr17059405qtk.253.1660645172443;
Tue, 16 Aug 2022 03:19:32 -0700 (PDT)
X-Received: by 2002:a05:6808:1202:b0:322:dc37:2c3b with SMTP id
a2-20020a056808120200b00322dc372c3bmr11914938oil.298.1660645172133; Tue, 16
Aug 2022 03:19:32 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 03:19:31 -0700 (PDT)
In-Reply-To: <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7744:c77e:1892:c183:a65f:8f2c;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7744:c77e:1892:c183:a65f:8f2c
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com>
<be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com> <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 16 Aug 2022 10:19:32 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8443

by: WM - Tue, 16 Aug 2022 10:19 UTC

Re: Natural numbers and vases III

<6ce5dba6-4a47-453e-969f-7f94ecd8be6en@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109271&group=sci.math#109271

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:a88a:0:b0:474:7f16:f272 with SMTP id x10-20020a0ca88a000000b004747f16f272mr17049383qva.4.1660646201498;
Tue, 16 Aug 2022 03:36:41 -0700 (PDT)
X-Received: by 2002:a05:6808:13d0:b0:343:56a3:cc2b with SMTP id
d16-20020a05680813d000b0034356a3cc2bmr9507348oiw.99.1660646201127; Tue, 16
Aug 2022 03:36:41 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 03:36:40 -0700 (PDT)
In-Reply-To: <169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=185.219.140.166; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 185.219.140.166
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com>
<be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com> <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
<169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <6ce5dba6-4a47-453e-969f-7f94ecd8be6en@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Tue, 16 Aug 2022 10:36:41 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8725

by: zelos...@gmail.com - Tue, 16 Aug 2022 10:36 UTC

Re: Natural numbers and vases III

<2f7c73fb-46d2-4802-8550-c7c81a028545n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109273&group=sci.math#109273

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:1537:b0:6ba:be3d:d70f with SMTP id n23-20020a05620a153700b006babe3dd70fmr14475891qkk.578.1660647319049;
Tue, 16 Aug 2022 03:55:19 -0700 (PDT)
X-Received: by 2002:a05:6830:18f1:b0:637:1578:5a37 with SMTP id
d17-20020a05683018f100b0063715785a37mr7370218otf.243.1660647318810; Tue, 16
Aug 2022 03:55:18 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 03:55:18 -0700 (PDT)
In-Reply-To: <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.189; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.189
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <2f7c73fb-46d2-4802-8550-c7c81a028545n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Tue, 16 Aug 2022 10:55:19 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8251

by: Gus Gassmann - Tue, 16 Aug 2022 10:55 UTC

Re: Natural numbers and vases III

<053558fd-4236-47bc-8580-ebb9eff47364n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109274&group=sci.math#109274

copy link Newsgroups: sci.math

X-Received: by 2002:ae9:e903:0:b0:6ba:e5aa:d59e with SMTP id x3-20020ae9e903000000b006bae5aad59emr11588543qkf.214.1660647539747;
Tue, 16 Aug 2022 03:58:59 -0700 (PDT)
X-Received: by 2002:a05:6870:338e:b0:f3:1a36:9485 with SMTP id
w14-20020a056870338e00b000f31a369485mr12775008oae.277.1660647539500; Tue, 16
Aug 2022 03:58:59 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 03:58:59 -0700 (PDT)
In-Reply-To: <169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.189; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.189
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<6df90f0b-fc4e-4175-ba6d-648e90f2a2a4n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com>
<be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com> <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
<169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <053558fd-4236-47bc-8580-ebb9eff47364n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Tue, 16 Aug 2022 10:58:59 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8205

by: Gus Gassmann - Tue, 16 Aug 2022 10:58 UTC

Re: Natural numbers and vases III

<tdg1kt$21he$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109278&group=sci.math#109278

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 16 Aug 2022 08:13:14 -0400
Organization: Peripheral Visions
Lines: 10
Message-ID: <tdg1kt$21he$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com> <8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com> <25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com> <abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com> <d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com> <fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com> <615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com> <f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com> <f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com> <0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com> <6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com> <7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com> <34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com> <b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com> <be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com> <d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com> <169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 16 Aug 2022 12:13:18 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="2a367e39047d2d0779c976304ff91bbb";
logging-data="67118"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+g7OfNBsGIwGdK4xlmhqCXB4B2McG7HhU="
Cancel-Lock: sha1:av4pPdG+d86a0I611XqgL4Hp8/o=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Tue, 16 Aug 2022 12:13 UTC

Re: Natural numbers and vases III

<tdg1l8$hdv$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109279&group=sci.math#109279

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 16 Aug 2022 07:13:26 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tdg1l8$hdv$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<8ccbc941-367e-4e0a-bc2a-9189d23f71d9n@googlegroups.com>
<25a961f1-e24d-409b-b581-ae597b5ff10cn@googlegroups.com>
<abc13c43-2e99-4934-8671-38caa3f0e908n@googlegroups.com>
<d3e204fd-bd43-4e5b-b296-357e133f637en@googlegroups.com>
<fcd89499-05a7-4477-9d63-d3e12ad78943n@googlegroups.com>
<615099e9-e0c9-44fe-9f6c-d95bd6f5b9a0n@googlegroups.com>
<f7a0ac33-2d4c-444e-8615-1b30bc532e83n@googlegroups.com>
<f84038fd-7d5d-403d-b7eb-169e5fc17282n@googlegroups.com>
<0aac575b-451a-4978-8405-ad4eec417b57n@googlegroups.com>
<6bd5bc2f-60a7-4f14-8af8-bfcbd29a716bn@googlegroups.com>
<7fb160fc-59a4-4a31-9189-92306a06439an@googlegroups.com>
<34392808-b956-4405-bcd6-3402b32ae4c1n@googlegroups.com>
<b295b64a-a7d5-4824-ad7f-85b4ec424364n@googlegroups.com>
<be7f0642-cde7-40b6-9ca4-dc8d2c87cc08n@googlegroups.com>
<d369b5bc-4e71-464e-b485-186c5968a70en@googlegroups.com>
<169efaf4-8bf7-40c5-8ac6-3671a943aac2n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="17855"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Tue, 16 Aug 2022 12:13 UTC

Re: Natural numbers and vases III

<bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109293&group=sci.math#109293

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:128a:b0:6bb:5a52:6dd8 with SMTP id w10-20020a05620a128a00b006bb5a526dd8mr3556792qki.350.1660661405175;
Tue, 16 Aug 2022 07:50:05 -0700 (PDT)
X-Received: by 2002:a05:6870:c598:b0:108:b7e2:ac8 with SMTP id
ba24-20020a056870c59800b00108b7e20ac8mr13577435oab.1.1660661404925; Tue, 16
Aug 2022 07:50:04 -0700 (PDT)
Path: i2pn2.org!i2pn.org!paganini.bofh.team!pasdenom.info!nntpfeed.proxad.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 07:50:04 -0700 (PDT)
In-Reply-To: <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Tue, 16 Aug 2022 14:50:05 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

by: William - Tue, 16 Aug 2022 14:50 UTC

Re: Natural numbers and vases III

<11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109295&group=sci.math#109295

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:5c91:0:b0:31f:2385:3633 with SMTP id r17-20020ac85c91000000b0031f23853633mr18609909qta.674.1660664344959;
Tue, 16 Aug 2022 08:39:04 -0700 (PDT)
X-Received: by 2002:a05:6870:b68f:b0:10b:ba83:92d4 with SMTP id
cy15-20020a056870b68f00b0010bba8392d4mr13058088oab.130.1660664344686; Tue, 16
Aug 2022 08:39:04 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.misty.com!border-2.nntp.ord.giganews.com!border-1.nntp.ord.giganews.com!nntp.giganews.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 08:39:04 -0700 (PDT)
In-Reply-To: <bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7744:c77e:1892:c183:a65f:8f2c;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7744:c77e:1892:c183:a65f:8f2c
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
<bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 16 Aug 2022 15:39:04 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 33

by: WM - Tue, 16 Aug 2022 15:39 UTC

Re: Natural numbers and vases III

<1ebd8258-357e-4da1-9357-f4d492a993cen@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109296&group=sci.math#109296

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:d07:b0:476:c32f:f4f4 with SMTP id 7-20020a0562140d0700b00476c32ff4f4mr18384946qvh.11.1660664466044;
Tue, 16 Aug 2022 08:41:06 -0700 (PDT)
X-Received: by 2002:a05:6870:8890:b0:101:db34:3ed6 with SMTP id
m16-20020a056870889000b00101db343ed6mr13995796oam.151.1660664465817; Tue, 16
Aug 2022 08:41:05 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!border-2.nntp.ord.giganews.com!border-1.nntp.ord.giganews.com!nntp.giganews.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 08:41:05 -0700 (PDT)
In-Reply-To: <bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.200.39; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.200.39
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
<bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1ebd8258-357e-4da1-9357-f4d492a993cen@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Tue, 16 Aug 2022 15:41:06 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 9

by: Fritz Feldhase - Tue, 16 Aug 2022 15:41 UTC

Re: Natural numbers and vases III

<tdgead$3b95$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109297&group=sci.math#109297

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 16 Aug 2022 11:49:30 -0400
Organization: Peripheral Visions
Lines: 29
Message-ID: <tdgead$3b95$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com> <d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com> <16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com> <d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com> <2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com> <47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com> <19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com> <814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com> <bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com> <11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 16 Aug 2022 15:49:34 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="2a367e39047d2d0779c976304ff91bbb";
logging-data="109861"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+EwH0syVf9svtHoU5sA4s/G5Ew2YMLKZU="
Cancel-Lock: sha1:BRGWfAIAEVT7R3PP0CW2RyryHhM=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb

by: FromTheRafters - Tue, 16 Aug 2022 15:49 UTC

Re: Natural numbers and vases III

<tdgikh$1pii$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109300&group=sci.math#109300

copy link Newsgroups: sci.math

Path: i2pn2.org!rocksolid2!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 16 Aug 2022 12:03:10 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tdgikh$1pii$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com>
<c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com>
<39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com>
<7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com>
<b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
<3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com>
<aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com>
<232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
<bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com>
<11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="58962"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US

by: Sergio - Tue, 16 Aug 2022 17:03 UTC

On 8/16/2022 10:39 AM, WM wrote:
> William schrieb am Dienstag, 16. August 2022 um 16:50:08 UTC+2:
>> On Tuesday, August 16, 2022 at 7:10:30 AM UTC-3, WM wrote:
>>> William schrieb am Montag, 15. August 2022 um 22:02:03 UTC+2:
>>>> On Monday, August 15, 2022 at 4:09:52 PM UTC-3, WM wrote:
>>>>
>>>>> Subtract all.
>>>>
>>>> Ok, Subtract the set.
>>> The set is all its elements.Therefore subtract the set means subtract all its elements.
>>>>> Then you can say: I have subtracted all Peano numbers
>>>> "All Peano Numbers" is the set of Peano numbers". This set contains S(n) for any element n. So if you remove the set you remove each S(n).
>>> And if you remove each S(n) then nothing remains.
>> Correct. If you "subtract all" then nothing remains. So your contention
>>
>>> Subtract all. Then you can say: I have subtracted all Peano numbers but most Peano numbers remain as successors
>>
>> is false.
>
> No. Individual subtraction leaves all dark numers.

hogwash

>
>> There is no contradiction. "all n which belong to a Peano set and have ℵo successors" is one set
>
> No, if so, then you could remove them by induction, individually. But you can't. The successors form an ℵ₀-set. The Peano numbers cannot leave the finite domain.
> Proof: {1, 2, 3, ..., n} is finite for every Peano number, for every definable Peano number n.

you have some of the words, but you do not seem to put them in order to actually mean something.

your proof is SPOOF, => {1, 2, 3, ..., n,...} is infinite for every Peano number

or you are cornered, you have run out of math, and are panicking, and then blurt out a fat red herring....

Perhaps if you use the language of MATH instead...

>
> Regards, wm

Re: Natural numbers and vases III

<c274bde0-1908-457f-a301-b07e61001b7cn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109301&group=sci.math#109301

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:f5d2:0:b0:475:825:757f with SMTP id q18-20020a0cf5d2000000b004750825757fmr18679592qvm.36.1660670736129;
Tue, 16 Aug 2022 10:25:36 -0700 (PDT)
X-Received: by 2002:a05:6870:328d:b0:10d:ce86:ceee with SMTP id
q13-20020a056870328d00b0010dce86ceeemr14127497oac.80.1660670735956; Tue, 16
Aug 2022 10:25:35 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 16 Aug 2022 10:25:35 -0700 (PDT)
In-Reply-To: <11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com> <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
<a4389406-8c8d-42d7-906f-1028e5a1ee7cn@googlegroups.com> <03241abe-f2f9-492b-81f6-860ebbe40711n@googlegroups.com>
<d618e3bb-c44f-4001-b669-3ca49e19df4fn@googlegroups.com> <c5dfef72-1c65-48d2-9173-d045360df7f7n@googlegroups.com>
<2756ffeb-0cc4-4185-99d7-2087b026301dn@googlegroups.com> <6d9e1f25-7761-4248-89e9-f7bbc206fcefn@googlegroups.com>
<52742c6d-bbc4-45e9-8a7b-edd3fd22ba2fn@googlegroups.com> <badc2d25-59cd-42eb-80e1-77b576b47339n@googlegroups.com>
<89e76263-96ae-4273-9669-bf3fb941ed95n@googlegroups.com> <210b8f70-9034-45ab-a4bc-c7b6bf8c3b24n@googlegroups.com>
<4e3200d9-c4a8-4d66-8957-0fd4965c8124n@googlegroups.com> <a250e05c-bbf1-4820-9f98-c7d84f2e5227n@googlegroups.com>
<21dc8e29-1244-4310-a58b-2a997be6a4ben@googlegroups.com> <dd54651b-2122-401b-9db7-340043c57289n@googlegroups.com>
<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com> <c1245e01-9a96-4dc4-9ef0-d58f9bd99fa5n@googlegroups.com>
<16481287-098f-4a75-be12-618a7db7e548n@googlegroups.com> <39b2d9a8-c2da-4d90-873e-b036b5fa38e3n@googlegroups.com>
<d9db1b1c-d666-46e0-a9dc-29306c0b6444n@googlegroups.com> <7f0ff1a5-cfdb-4d11-8b78-021d1e18529fn@googlegroups.com>
<2463ec1b-e7a5-403d-8e4e-9abbb2cfca5an@googlegroups.com> <b131a063-fff8-46e5-a77e-22c01d365da8n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com> <3304c47f-f4e6-4a7d-a1fd-63c5a4776263n@googlegroups.com>
<19f5c06d-fc4a-451d-8b68-b7a8e434acf4n@googlegroups.com> <aae3789d-2d80-438e-82b7-0380d19000d3n@googlegroups.com>
<814ffa11-3523-48b0-8352-b51808f5b196n@googlegroups.com> <232a23f4-2c8b-4cf0-9c99-d5ef6d4a8c25n@googlegroups.com>
<bb46b9cc-bd4f-40e7-b81c-90e69bc5936an@googlegroups.com> <11f33099-3b5f-42a1-bd2a-d18966571389n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <c274bde0-1908-457f-a301-b07e61001b7cn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Tue, 16 Aug 2022 17:25:36 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

by: William - Tue, 16 Aug 2022 17:25 UTC

Life is difficult because it is non-linear.

tech / sci.math / Re: Natural numbers and vases III

tech / sci.math / Re: Natural numbers and vases III

Subject	Author
Natural numbers and vases III	WM
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Africani
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eduardo Faqtardo
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Archimedes Plutonium
Re: Natural numbers and vases III	Archimedes Plutonium