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

Re: Natural numbers and vases III

<41223ae9-d644-4560-8048-dbf9680747ben@googlegroups.com>

https://www.novabbs.com/tech/article-flat.php?id=108249&group=sci.math#108249

X-Received: by 2002:a05:620a:4310:b0:6ac:f9df:178d with SMTP id u16-20020a05620a431000b006acf9df178dmr5833893qko.773.1659717584102;
Fri, 05 Aug 2022 09:39:44 -0700 (PDT)
X-Received: by 2002:a05:6870:15c3:b0:ed:9d61:a56c with SMTP id
k3-20020a05687015c300b000ed9d61a56cmr3596565oad.152.1659717583918; Fri, 05
Aug 2022 09:39:43 -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: Fri, 5 Aug 2022 09:39:43 -0700 (PDT)
In-Reply-To: <62ed462e$0$24820$426a74cc@news.free.fr>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec67:88a4:1507:4aaa:883e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec67:88a4:1507:4aaa:883e
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<62ed4270$0$22068$426a34cc@news.free.fr> <b4cb3907-0902-472b-8122-bf00ba9b0030n@googlegroups.com>
<62ed462e$0$24820$426a74cc@news.free.fr>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <41223ae9-d644-4560-8048-dbf9680747ben@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 05 Aug 2022 16:39:44 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 2735

by: WM - Fri, 5 Aug 2022 16:39 UTC

Re: Natural numbers and vases III

<ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108252&group=sci.math#108252

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:598e:0:b0:33c:9c91:2f0e with SMTP id e14-20020ac8598e000000b0033c9c912f0emr6605679qte.213.1659718238422;
Fri, 05 Aug 2022 09:50:38 -0700 (PDT)
X-Received: by 2002:a05:6870:328d:b0:10d:ce86:ceee with SMTP id
q13-20020a056870328d00b0010dce86ceeemr7388355oac.80.1659718238233; Fri, 05
Aug 2022 09:50:38 -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: Fri, 5 Aug 2022 09:50:38 -0700 (PDT)
In-Reply-To: <816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec67:88a4:1507:4aaa:883e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec67:88a4:1507:4aaa:883e
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 05 Aug 2022 16:50:38 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7851

by: WM - Fri, 5 Aug 2022 16:50 UTC

William schrieb am Freitag, 5. August 2022 um 18:33:10 UTC+2:
> On Friday, August 5, 2022 at 1:11:23 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> > > On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > > > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> >
> > > > All individually definable endsegments have infinite intersection.
> > > Nope.
> >
> > Then define individually endsegments which have an empty intersection.
> We need to deal with an infinite number of things.

But we can individually define only a finite number of things.

> So we use a method, induction, that can deal with an infinite number of things.

Induction proves properties of natural numbers which have a finite distance from 0 and therefore belong to a finite set with no upper bound.

Cantor claimed actualinfinity. ω, the first infinite ordinal, has infinite distance from 0. That means that actually infinitely many natural numbers are in between, more than could be object to induction.

> Use induction to show each endsegment in the set of endsegments is "individually definable".

Impossible. If it were possible, then induction would be useless because wrong. Proof by the impossibility to define individually all natural numbers such that none remains.

Every definable natural number has ℵo successors most of which are undefinable.

"Every definable natural number has ℵo definable successors" is nonsense. It is not possible that all are definable although almost all are not.

> The set of endsegment is thus a set of "individually definable endsegments" and is the set you asked for.

No, this set has the property |∩{E(k) : k ∈ ℕ_def}| = ℵ₀

I asked for ∩{E(k) : k ∈ ℕ} = { } and how this could be reached with respect to

∀k ∈ ℕ: E(k+1) = E(k) \ {k}

Regards, WM

Re: Natural numbers and vases III

<tcjhph$sa9$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108253&group=sci.math#108253

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: Fri, 5 Aug 2022 11:50:56 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcjhph$sa9$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com>
<c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com>
<aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>
<5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
<87cb81be-b717-4aba-b328-0a9c5bf96a61n@googlegroups.com>
<8f30bbb4-6796-4388-9eb7-f8aa2fdf7276n@googlegroups.com>
<ceb407f7-f8fc-4932-be6b-af172bd6d3c9n@googlegroups.com>
<f0845f26-df7c-4ac7-88be-c9ab7ef91f1en@googlegroups.com>
<tcgvj4$486$1@gioia.aioe.org>
<69924d0e-3da9-4b33-81d1-151bf8257333n@googlegroups.com>
<5389da56-c7ef-494f-8ff2-6e12d0ea9fddn@googlegroups.com>
<c8f8a60a-aa7d-4025-b01a-1da51811f46cn@googlegroups.com>
<3b425dc5-182e-4929-a1c9-95a6cdec4014n@googlegroups.com>
<c1461600-4ed2-4124-890c-05c4f3e7d46fn@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="29001"; 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 - Fri, 5 Aug 2022 16:50 UTC

On 8/5/2022 11:28 AM, WM wrote:
> Gus Gassmann schrieb am Freitag, 5. August 2022 um 18:21:25 UTC+2:
>> On Friday, 5 August 2022 at 13:15:49 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 20:51:33 UTC+2:
>>>
>>>> Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/.
>>> Define enough endsegments individually such that their intersection is empty. Fail.
>> Show me an undefinable end segment individually. Fail.
>
> Chuckle.
>
> There is no white which is black. But I can prove the existence of dark endsegments. You can ony claim your wrong claim.
>
> Proof: It is impossible to remove from the set of endsegments {E(1), E(2), ...} so many endsegments that the intersection is empty
> ∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }
> but removing another definable endsegment E(X+1) would change the result.
>
> Regards, WM
>
>

I fix;

∩({E(1), E(2), E(3), ...}) = { }

see? no X, X+1, nor any "definable" crap fake math needed.

Extra Credit Problem, Prove the above.

Re: Natural numbers and vases III

<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108257&group=sci.math#108257

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:d62:b0:474:7ceb:247e with SMTP id 2-20020a0562140d6200b004747ceb247emr6423881qvs.61.1659719217809;
Fri, 05 Aug 2022 10:06:57 -0700 (PDT)
X-Received: by 2002:a05:6830:6613:b0:61c:acf8:8e41 with SMTP id
cp19-20020a056830661300b0061cacf88e41mr2800700otb.298.1659719217576; Fri, 05
Aug 2022 10:06:57 -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: Fri, 5 Aug 2022 10:06:57 -0700 (PDT)
In-Reply-To: <ba929c70-156b-4950-a9d0-5f981636eaefn@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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Fri, 05 Aug 2022 17:06:57 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 7003

by: William - Fri, 5 Aug 2022 17:06 UTC

On Friday, August 5, 2022 at 1:50:43 PM UTC-3, WM wrote:
> William schrieb am Freitag, 5. August 2022 um 18:33:10 UTC+2:
> > On Friday, August 5, 2022 at 1:11:23 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> > > > On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> > >
> > > > > All individually definable endsegments have infinite intersection.
> > > > Nope.
> > >
> > > Then define individually endsegments which have an empty intersection.
> > We need to deal with an infinite number of things.
> But we can individually define only a finite number of things.

However, we can know that each element of an infinite set is "individually definable". That is all we need to know that a set of "individually definable endsegments" has empty intersection.

.... the impossibility to [write down] all natural numbers such that none remains.

So what? We know that we cannot write down an infinite number of natural numbers. However, we can know that each natural number
has the property that it can be written down (independent of time and resources).

--
William Hughes

Re: Natural numbers and vases III

<59e50ad4-5f1d-4b46-9900-7205b225ee17n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108258&group=sci.math#108258

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1456:b0:31f:a93:e030 with SMTP id v22-20020a05622a145600b0031f0a93e030mr6588023qtx.432.1659719889596;
Fri, 05 Aug 2022 10:18:09 -0700 (PDT)
X-Received: by 2002:a05:6808:13d2:b0:33a:7651:3ab3 with SMTP id
d18-20020a05680813d200b0033a76513ab3mr6514786oiw.277.1659719889296; Fri, 05
Aug 2022 10:18:09 -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: Fri, 5 Aug 2022 10:18:09 -0700 (PDT)
In-Reply-To: <c1461600-4ed2-4124-890c-05c4f3e7d46fn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com> <e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net> <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net> <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com> <5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
<87cb81be-b717-4aba-b328-0a9c5bf96a61n@googlegroups.com> <8f30bbb4-6796-4388-9eb7-f8aa2fdf7276n@googlegroups.com>
<ceb407f7-f8fc-4932-be6b-af172bd6d3c9n@googlegroups.com> <f0845f26-df7c-4ac7-88be-c9ab7ef91f1en@googlegroups.com>
<tcgvj4$486$1@gioia.aioe.org> <69924d0e-3da9-4b33-81d1-151bf8257333n@googlegroups.com>
<5389da56-c7ef-494f-8ff2-6e12d0ea9fddn@googlegroups.com> <c8f8a60a-aa7d-4025-b01a-1da51811f46cn@googlegroups.com>
<3b425dc5-182e-4929-a1c9-95a6cdec4014n@googlegroups.com> <c1461600-4ed2-4124-890c-05c4f3e7d46fn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <59e50ad4-5f1d-4b46-9900-7205b225ee17n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Fri, 05 Aug 2022 17:18:09 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 2957

by: Gus Gassmann - Fri, 5 Aug 2022 17:18 UTC

Re: Natural numbers and vases III

<89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108259&group=sci.math#108259

copy link Newsgroups: sci.math

X-Received: by 2002:a37:be42:0:b0:6b5:e542:233b with SMTP id o63-20020a37be42000000b006b5e542233bmr6292272qkf.498.1659722700479;
Fri, 05 Aug 2022 11:05:00 -0700 (PDT)
X-Received: by 2002:a05:6870:2483:b0:ed:f721:2734 with SMTP id
s3-20020a056870248300b000edf7212734mr3687444oaq.242.1659722700255; Fri, 05
Aug 2022 11:05:00 -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: Fri, 5 Aug 2022 11:05:00 -0700 (PDT)
In-Reply-To: <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.198.116; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.198.116
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Fri, 05 Aug 2022 18:05:00 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6046

by: Fritz Feldhase - Fri, 5 Aug 2022 18:05 UTC

Re: Natural numbers and vases III

<a598e437-9354-4ec2-9d22-60777e071879n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108260&group=sci.math#108260

copy link Newsgroups: sci.math

X-Received: by 2002:a37:b983:0:b0:6b8:ddba:f27e with SMTP id j125-20020a37b983000000b006b8ddbaf27emr6085117qkf.774.1659725020585;
Fri, 05 Aug 2022 11:43:40 -0700 (PDT)
X-Received: by 2002:a05:6808:198a:b0:33f:46b4:9f0b with SMTP id
bj10-20020a056808198a00b0033f46b49f0bmr3521581oib.242.1659725020332; Fri, 05
Aug 2022 11:43:40 -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: Fri, 5 Aug 2022 11:43:40 -0700 (PDT)
In-Reply-To: <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2603:7080:aff0:60:289f:139f:d4e7:51a4;
posting-account=I6O9nAoAAABb1i1LpKMPS-CPmVJHIbyE
NNTP-Posting-Host: 2603:7080:aff0:60:289f:139f:d4e7:51a4
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <a598e437-9354-4ec2-9d22-60777e071879n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
Injection-Date: Fri, 05 Aug 2022 18:43:40 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8276

by: Eram semper recta - Fri, 5 Aug 2022 18:43 UTC

On Friday, 5 August 2022 at 12:50:43 UTC-4, WM wrote:
> William schrieb am Freitag, 5. August 2022 um 18:33:10 UTC+2:
> > On Friday, August 5, 2022 at 1:11:23 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> > > > On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> > >
> > > > > All individually definable endsegments have infinite intersection..
> > > > Nope.
> > >
> > > Then define individually endsegments which have an empty intersection..
> > We need to deal with an infinite number of things.
> But we can individually define only a finite number of things.
> > So we use a method, induction, that can deal with an infinite number of things.
> Induction proves properties of natural numbers which have a finite distance from 0 and therefore belong to a finite set with no upper bound.
>
> Cantor claimed actualinfinity. ω, the first infinite ordinal, has infinite distance from 0. That means that actually infinitely many natural numbers are in between, more than could be object to induction.
> > Use induction to show each endsegment in the set of endsegments is "individually definable".
> Impossible. If it were possible, then induction would be useless because wrong. Proof by the impossibility to define individually all natural numbers such that none remains.
>
> Every definable natural number has ℵo successors most of which are undefinable.
>
> "Every definable natural number has ℵo definable successors" is nonsense. It is not possible that all are definable although almost all are not.
> > The set of endsegment is thus a set of "individually definable endsegments" and is the set you asked for.
> No, this set has the property |∩{E(k) : k ∈ ℕ_def}| = ℵ₀
>
> I asked for ∩{E(k) : k ∈ ℕ} = { } and how this could be reached with respect to
>
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k}

The more you correct the idiots, the more defiant they become. In America we have this phenomenon among Trump supporters.

A crank is one who cannot be convinced in the face of overwhelming evidence..

>
> Regards, WM

Re: Natural numbers and vases III

<9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108261&group=sci.math#108261

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:258c:b0:476:6879:eade with SMTP id fq12-20020a056214258c00b004766879eademr6768562qvb.69.1659725407104;
Fri, 05 Aug 2022 11:50:07 -0700 (PDT)
X-Received: by 2002:a05:6808:d4e:b0:33a:a53c:5480 with SMTP id
w14-20020a0568080d4e00b0033aa53c5480mr6878522oik.151.1659725406862; Fri, 05
Aug 2022 11:50:06 -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: Fri, 5 Aug 2022 11:50:06 -0700 (PDT)
In-Reply-To: <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Fri, 05 Aug 2022 18:50:07 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6259

by: Gus Gassmann - Fri, 5 Aug 2022 18:50 UTC

Re: Natural numbers and vases III

<tcjq3r$3a9su$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108265&group=sci.math#108265

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: Fri, 05 Aug 2022 15:12:52 -0400
Organization: Peripheral Visions
Lines: 15
Message-ID: <tcjq3r$3a9su$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <89b4c406-158e-4af2-a415-d540a0e92648n@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: Fri, 5 Aug 2022 19:12:59 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="fe6d591363925f89dc52b1a97b242cce";
logging-data="3483550"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+lJA+VJIAIMQs2WNuPaktMwuR9Xe5I5n0="
Cancel-Lock: sha1:UM+b13Tw46ENz0s8U7S1yoAw+ls=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Fri, 5 Aug 2022 19:12 UTC

Re: Natural numbers and vases III

<d2ba9cc4-9df2-4299-addd-6e8450c39c0fn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108266&group=sci.math#108266

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:df82:0:b0:474:97e5:4951 with SMTP id w2-20020a0cdf82000000b0047497e54951mr7017030qvl.96.1659728176914;
Fri, 05 Aug 2022 12:36:16 -0700 (PDT)
X-Received: by 2002:a05:6870:f706:b0:113:665a:b15b with SMTP id
ej6-20020a056870f70600b00113665ab15bmr1235140oab.293.1659728176631; Fri, 05
Aug 2022 12:36:16 -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: Fri, 5 Aug 2022 12:36:16 -0700 (PDT)
In-Reply-To: <ba929c70-156b-4950-a9d0-5f981636eaefn@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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d2ba9cc4-9df2-4299-addd-6e8450c39c0fn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Fri, 05 Aug 2022 19:36:16 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6013

by: William - Fri, 5 Aug 2022 19:36 UTC

Re: Natural numbers and vases III

<b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108306&group=sci.math#108306

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:e185:0:b0:474:7ab8:1eaf with SMTP id p5-20020a0ce185000000b004747ab81eafmr9188186qvl.76.1659782962303;
Sat, 06 Aug 2022 03:49:22 -0700 (PDT)
X-Received: by 2002:a05:6808:238d:b0:33a:7c9b:a1c7 with SMTP id
bp13-20020a056808238d00b0033a7c9ba1c7mr4630097oib.7.1659782962072; Sat, 06
Aug 2022 03:49:22 -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: Sat, 6 Aug 2022 03:49:21 -0700 (PDT)
In-Reply-To: <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 10:49:22 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7774

by: WM - Sat, 6 Aug 2022 10:49 UTC

William schrieb am Freitag, 5. August 2022 um 19:07:03 UTC+2:
> On Friday, August 5, 2022 at 1:50:43 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 5. August 2022 um 18:33:10 UTC+2:
> > > On Friday, August 5, 2022 at 1:11:23 PM UTC-3, WM wrote:
> > > > William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> > > > > On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > > > > > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> > > >
> > > > > > All individually definable endsegments have infinite intersection.
> > > > > Nope.
> > > >
> > > > Then define individually endsegments which have an empty intersection.
> > > We need to deal with an infinite number of things.
> > But we can individually define only a finite number of things.
> However, we can know that each element of an infinite set is "individually definable". That is all we need to know that a set of "individually definable endsegments" has empty intersection.

You are wrong. Overwhelming evidence speaks against your opinion. By the way defining is proved by defining, not by "proving" definability in a rotten system.
>
> ... the impossibility to [write down] all natural numbers such that none remains.
>
> So what? We know that we cannot write down an infinite number of natural numbers. However, we can know that each natural number
> has the property that it can be written down (independent of time and resources).

Counter evidendence: Every definable endsegment can be removed from the set of endsegments. Nevertheless there remain infinitely many which yield an empty intersection. If you were right, you could remove one of them individually such that the intersection is no longer empty.

One of them would be enough!

Regards, WM

Re: Natural numbers and vases III

<b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108308&group=sci.math#108308

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5b8d:0:b0:47b:2c2c:96f with SMTP id 13-20020ad45b8d000000b0047b2c2c096fmr941402qvp.80.1659785706604;
Sat, 06 Aug 2022 04:35:06 -0700 (PDT)
X-Received: by 2002:a05:6870:b68f:b0:10b:ba83:92d4 with SMTP id
cy15-20020a056870b68f00b0010bba8392d4mr8207661oab.130.1659785706321; Sat, 06
Aug 2022 04:35:06 -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: Sat, 6 Aug 2022 04:35:06 -0700 (PDT)
In-Reply-To: <9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
<9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 11:35:06 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6847

by: WM - Sat, 6 Aug 2022 11:35 UTC

Re: Natural numbers and vases III

<1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108309&group=sci.math#108309

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:4017:b0:476:6229:bbf8 with SMTP id kd23-20020a056214401700b004766229bbf8mr9213674qvb.14.1659786195819;
Sat, 06 Aug 2022 04:43:15 -0700 (PDT)
X-Received: by 2002:aca:b60a:0:b0:342:894c:2277 with SMTP id
g10-20020acab60a000000b00342894c2277mr4788935oif.43.1659786195597; Sat, 06
Aug 2022 04:43:15 -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: Sat, 6 Aug 2022 04:43:15 -0700 (PDT)
In-Reply-To: <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
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>
<9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com> <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 06 Aug 2022 11:43:15 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6622

by: Gus Gassmann - Sat, 6 Aug 2022 11:43 UTC

Re: Natural numbers and vases III

<1aad1da6-eaf1-4c61-9a99-cd5cb773da79n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108310&group=sci.math#108310

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1a11:b0:341:4c47:8cc2 with SMTP id f17-20020a05622a1a1100b003414c478cc2mr9377863qtb.175.1659786280227;
Sat, 06 Aug 2022 04:44:40 -0700 (PDT)
X-Received: by 2002:a05:6870:8890:b0:101:db34:3ed6 with SMTP id
m16-20020a056870889000b00101db343ed6mr8728730oam.151.1659786279954; Sat, 06
Aug 2022 04:44:39 -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: Sat, 6 Aug 2022 04:44:39 -0700 (PDT)
In-Reply-To: <d2ba9cc4-9df2-4299-addd-6e8450c39c0fn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
<d2ba9cc4-9df2-4299-addd-6e8450c39c0fn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1aad1da6-eaf1-4c61-9a99-cd5cb773da79n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 11:44:40 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6359

by: WM - Sat, 6 Aug 2022 11:44 UTC

Re: Natural numbers and vases III

<50171581-d8bf-4bfb-94bb-5d024f65988bn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108311&group=sci.math#108311

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:512:b0:340:40fd:a16e with SMTP id l18-20020a05622a051200b0034040fda16emr9352214qtx.415.1659786552385;
Sat, 06 Aug 2022 04:49:12 -0700 (PDT)
X-Received: by 2002:a05:6830:2709:b0:61c:c396:94f2 with SMTP id
j9-20020a056830270900b0061cc39694f2mr4301174otu.369.1659786552169; Sat, 06
Aug 2022 04:49:12 -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: Sat, 6 Aug 2022 04:49:11 -0700 (PDT)
In-Reply-To: <1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
<9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com> <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>
<1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <50171581-d8bf-4bfb-94bb-5d024f65988bn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 11:49:12 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7057

by: WM - Sat, 6 Aug 2022 11:49 UTC

Gus Gassmann schrieb am Samstag, 6. August 2022 um 13:43:21 UTC+2:
> On Saturday, 6 August 2022 at 08:35:12 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Freitag, 5. August 2022 um 20:50:13 UTC+2:
> > > On Friday, 5 August 2022 at 13:50:43 UTC-3, WM wrote:
> > > [...]
> > > > Cantor claimed actualinfinity. ω, the first infinite ordinal, has infinite distance from 0. That means that actually infinitely many natural numbers are in between, more than could be object to induction.
> > > Three statements, all bullshit.
> >
> > All from Cantor.
> You have no idea what a distance is.

Here it is the number of numbers between 0 and ω.

> You have no idea how to interpret the distance between two points.

Here we talk about the sequence of natural numbers

> And you have no clue about induction.

There is no clue necessary if one knows a bit of mathematics. You appear to be not familiar with it. Try to study it. It is not that difficult as you might think.

Regards, WM

Re: Natural numbers and vases III

<7f4fc6a3-663a-4908-803b-0295a99da7aan@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108312&group=sci.math#108312

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:58b:b0:31f:407e:9e43 with SMTP id c11-20020a05622a058b00b0031f407e9e43mr9044365qtb.258.1659786698923;
Sat, 06 Aug 2022 04:51:38 -0700 (PDT)
X-Received: by 2002:a05:6808:aad:b0:342:9a85:882c with SMTP id
r13-20020a0568080aad00b003429a85882cmr6709978oij.80.1659786698734; Sat, 06
Aug 2022 04:51:38 -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: Sat, 6 Aug 2022 04:51:38 -0700 (PDT)
In-Reply-To: <89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
<89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <7f4fc6a3-663a-4908-803b-0295a99da7aan@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 11:51:38 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6371

by: WM - Sat, 6 Aug 2022 11:51 UTC

Re: Natural numbers and vases III

<ae84eed0-7deb-4af3-8c31-f91ac823f327n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108313&group=sci.math#108313

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:48b:b0:31f:2416:2f3f with SMTP id p11-20020a05622a048b00b0031f24162f3fmr9037046qtx.376.1659786893818;
Sat, 06 Aug 2022 04:54:53 -0700 (PDT)
X-Received: by 2002:a05:6808:1b8d:b0:32f:7995:b32b with SMTP id
cj13-20020a0568081b8d00b0032f7995b32bmr7701359oib.219.1659786893587; Sat, 06
Aug 2022 04:54:53 -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: Sat, 6 Aug 2022 04:54:53 -0700 (PDT)
In-Reply-To: <59e50ad4-5f1d-4b46-9900-7205b225ee17n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com> <e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net> <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net> <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com> <5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
<87cb81be-b717-4aba-b328-0a9c5bf96a61n@googlegroups.com> <8f30bbb4-6796-4388-9eb7-f8aa2fdf7276n@googlegroups.com>
<ceb407f7-f8fc-4932-be6b-af172bd6d3c9n@googlegroups.com> <f0845f26-df7c-4ac7-88be-c9ab7ef91f1en@googlegroups.com>
<tcgvj4$486$1@gioia.aioe.org> <69924d0e-3da9-4b33-81d1-151bf8257333n@googlegroups.com>
<5389da56-c7ef-494f-8ff2-6e12d0ea9fddn@googlegroups.com> <c8f8a60a-aa7d-4025-b01a-1da51811f46cn@googlegroups.com>
<3b425dc5-182e-4929-a1c9-95a6cdec4014n@googlegroups.com> <c1461600-4ed2-4124-890c-05c4f3e7d46fn@googlegroups.com>
<59e50ad4-5f1d-4b46-9900-7205b225ee17n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <ae84eed0-7deb-4af3-8c31-f91ac823f327n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 11:54:53 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3206

by: WM - Sat, 6 Aug 2022 11:54 UTC

Re: Natural numbers and vases III

<40a03e8a-4080-47f2-9841-54a6ee07744en@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108314&group=sci.math#108314

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4310:b0:6ac:f9df:178d with SMTP id u16-20020a05620a431000b006acf9df178dmr8350145qko.773.1659788859004;
Sat, 06 Aug 2022 05:27:39 -0700 (PDT)
X-Received: by 2002:aca:5d41:0:b0:342:ac18:e523 with SMTP id
r62-20020aca5d41000000b00342ac18e523mr4550809oib.130.1659788858804; Sat, 06
Aug 2022 05:27:38 -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: Sat, 6 Aug 2022 05:27:38 -0700 (PDT)
In-Reply-To: <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <40a03e8a-4080-47f2-9841-54a6ee07744en@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 12:27:39 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6450

by: WM - Sat, 6 Aug 2022 12:27 UTC

Re: Natural numbers and vases III

<tclmuq$3rkbs$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108315&group=sci.math#108315

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: Sat, 06 Aug 2022 08:31:15 -0400
Organization: Peripheral Visions
Lines: 19
Message-ID: <tclmuq$3rkbs$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com> <7f4fc6a3-663a-4908-803b-0295a99da7aan@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: Sat, 6 Aug 2022 12:31:22 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="4aa9660a0409d568d29a45454c5a20c4";
logging-data="4051324"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19VkFKrEy9FW0coqjG6aRp3ShlKMGdACfM="
Cancel-Lock: sha1:nK5OZfpxBEfgYxp5xKpaTL2CGj0=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Sat, 6 Aug 2022 12:31 UTC

Re: Natural numbers and vases III

<04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108316&group=sci.math#108316

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4690:b0:6b5:dbd5:e30 with SMTP id bq16-20020a05620a469000b006b5dbd50e30mr8343344qkb.35.1659789260064;
Sat, 06 Aug 2022 05:34:20 -0700 (PDT)
X-Received: by 2002:a9d:6344:0:b0:62d:4a87:9209 with SMTP id
y4-20020a9d6344000000b0062d4a879209mr4123286otk.130.1659789259823; Sat, 06
Aug 2022 05:34:19 -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: Sat, 6 Aug 2022 05:34:19 -0700 (PDT)
In-Reply-To: <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 12:34:20 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6191

by: WM - Sat, 6 Aug 2022 12:34 UTC

Re: Natural numbers and vases III

<tcln8b$3rmpo$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108317&group=sci.math#108317

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: Sat, 06 Aug 2022 08:36:20 -0400
Organization: Peripheral Visions
Lines: 31
Message-ID: <tcln8b$3rmpo$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com> <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com> <1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com> <50171581-d8bf-4bfb-94bb-5d024f65988bn@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: Sat, 6 Aug 2022 12:36:27 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="4aa9660a0409d568d29a45454c5a20c4";
logging-data="4053816"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19F9mKvVIvonPfQjlFgntrfmOMPLXktrAk="
Cancel-Lock: sha1:q7+346g56JvceN0caZ2XhHspNWM=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb

by: FromTheRafters - Sat, 6 Aug 2022 12:36 UTC

WM presented the following explanation :
> Gus Gassmann schrieb am Samstag, 6. August 2022 um 13:43:21 UTC+2:
>> On Saturday, 6 August 2022 at 08:35:12 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Freitag, 5. August 2022 um 20:50:13 UTC+2:
>>>> On Friday, 5 August 2022 at 13:50:43 UTC-3, WM wrote:
>>>> [...]
>>>>> Cantor claimed actualinfinity. ω, the first infinite ordinal, has
>>>>> infinite distance from 0. That means that actually infinitely many
>>>>> natural numbers are in between, more than could be object to induction.
>>>> Three statements, all bullshit.
>>>
>>> All from Cantor.
>> You have no idea what a distance is.
>
> Here it is the number of numbers between 0 and ω.

Countable infinity is not a 'natural' number.

>> You have no idea how to interpret the distance between two points.
>
> Here we talk about the sequence of natural numbers

The successor function exists without a metric.

>> And you have no clue about induction.
>
> There is no clue necessary if one knows a bit of mathematics. You appear to
> be not familiar with it. Try to study it. It is not that difficult as you
> might think.

The needle on my irony meter just wrapped around the peg.

Re: Natural numbers and vases III

<fb11cd43-b56a-4629-92ab-5e4406cfdf5an@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108318&group=sci.math#108318

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:58b:b0:31f:407e:9e43 with SMTP id c11-20020a05622a058b00b0031f407e9e43mr9182250qtb.258.1659789483727;
Sat, 06 Aug 2022 05:38:03 -0700 (PDT)
X-Received: by 2002:a9d:67d3:0:b0:636:c40e:1eb2 with SMTP id
c19-20020a9d67d3000000b00636c40e1eb2mr1445509otn.151.1659789483479; Sat, 06
Aug 2022 05:38:03 -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: Sat, 6 Aug 2022 05:38:03 -0700 (PDT)
In-Reply-To: <tclmuq$3rkbs$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:2c8a:b195:1d47:e22;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:2c8a:b195:1d47:e22
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com> <7f4fc6a3-663a-4908-803b-0295a99da7aan@googlegroups.com>
<tclmuq$3rkbs$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <fb11cd43-b56a-4629-92ab-5e4406cfdf5an@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 12:38:03 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 2704

by: WM - Sat, 6 Aug 2022 12:38 UTC

Re: Natural numbers and vases III

<tclo7u$3ruh7$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108319&group=sci.math#108319

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: Sat, 06 Aug 2022 08:53:11 -0400
Organization: Peripheral Visions
Lines: 11
Message-ID: <tclo7u$3ruh7$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <89b4c406-158e-4af2-a415-d540a0e92648n@googlegroups.com> <7f4fc6a3-663a-4908-803b-0295a99da7aan@googlegroups.com> <tclmuq$3rkbs$1@dont-email.me> <fb11cd43-b56a-4629-92ab-5e4406cfdf5an@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: Sat, 6 Aug 2022 12:53:19 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="4aa9660a0409d568d29a45454c5a20c4";
logging-data="4061735"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19fgkTwlLQw9d/nduhtzNSwJaKPKo0I+ow="
Cancel-Lock: sha1:ukj91WQ/u1E6InjUFZtyNcvS2Uw=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Sat, 6 Aug 2022 12:53 UTC

Re: Natural numbers and vases III

<c31c2266-9395-4877-bc2f-0b7c70b1f20cn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108323&group=sci.math#108323

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4248:b0:6a8:3259:6a76 with SMTP id w8-20020a05620a424800b006a832596a76mr8612092qko.175.1659795624996;
Sat, 06 Aug 2022 07:20:24 -0700 (PDT)
X-Received: by 2002:a9d:62d2:0:b0:636:94a9:2e23 with SMTP id
z18-20020a9d62d2000000b0063694a92e23mr4281798otk.167.1659795624781; Sat, 06
Aug 2022 07:20:24 -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: Sat, 6 Aug 2022 07:20:24 -0700 (PDT)
In-Reply-To: <50171581-d8bf-4bfb-94bb-5d024f65988bn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
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>
<9dc73b8c-d818-4e67-8199-41e450dfa943n@googlegroups.com> <b6fc45d7-1370-4cb3-9dba-269c6caaf4a6n@googlegroups.com>
<1bf00189-5567-4f42-b5a6-7e9d80e4430fn@googlegroups.com> <50171581-d8bf-4bfb-94bb-5d024f65988bn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <c31c2266-9395-4877-bc2f-0b7c70b1f20cn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 06 Aug 2022 14:20:24 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6358

by: Gus Gassmann - Sat, 6 Aug 2022 14:20 UTC

Re: Natural numbers and vases III

<c978ef12-efc2-430b-ae9c-750b375f707dn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108324&group=sci.math#108324

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:48b:b0:31f:2416:2f3f with SMTP id p11-20020a05622a048b00b0031f24162f3fmr9508501qtx.376.1659795856007;
Sat, 06 Aug 2022 07:24:16 -0700 (PDT)
X-Received: by 2002:a9d:7cc4:0:b0:61c:acaa:1c67 with SMTP id
r4-20020a9d7cc4000000b0061cacaa1c67mr4408867otn.311.1659795855761; Sat, 06
Aug 2022 07:24:15 -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: Sat, 6 Aug 2022 07:24:15 -0700 (PDT)
In-Reply-To: <ae84eed0-7deb-4af3-8c31-f91ac823f327n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com> <e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net> <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net> <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com> <5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
<87cb81be-b717-4aba-b328-0a9c5bf96a61n@googlegroups.com> <8f30bbb4-6796-4388-9eb7-f8aa2fdf7276n@googlegroups.com>
<ceb407f7-f8fc-4932-be6b-af172bd6d3c9n@googlegroups.com> <f0845f26-df7c-4ac7-88be-c9ab7ef91f1en@googlegroups.com>
<tcgvj4$486$1@gioia.aioe.org> <69924d0e-3da9-4b33-81d1-151bf8257333n@googlegroups.com>
<5389da56-c7ef-494f-8ff2-6e12d0ea9fddn@googlegroups.com> <c8f8a60a-aa7d-4025-b01a-1da51811f46cn@googlegroups.com>
<3b425dc5-182e-4929-a1c9-95a6cdec4014n@googlegroups.com> <c1461600-4ed2-4124-890c-05c4f3e7d46fn@googlegroups.com>
<59e50ad4-5f1d-4b46-9900-7205b225ee17n@googlegroups.com> <ae84eed0-7deb-4af3-8c31-f91ac823f327n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <c978ef12-efc2-430b-ae9c-750b375f707dn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 06 Aug 2022 14:24:16 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3600

by: Gus Gassmann - Sat, 6 Aug 2022 14:24 UTC

"Your butt is mine." -- Michael Jackson, Bad

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