Message-ID:

Never make anything simple and efficient when a way can be found to make it complex and wonderful.

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

Re: Natural numbers and vases III

<tclu1b$15jo$1@gioia.aioe.org>

https://www.novabbs.com/tech/article-flat.php?id=108325&group=sci.math#108325

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: Sat, 6 Aug 2022 09:32:09 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tclu1b$15jo$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="38520"; 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 - Sat, 6 Aug 2022 14:32 UTC

On 8/6/2022 6:54 AM, WM wrote:
> Gus Gassmann schrieb am Freitag, 5. August 2022 um 19:18:14 UTC+2:
>> On Friday, 5 August 2022 at 13:28:30 UTC-3, WM wrote:
>> [...]
>>> 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.
>> If you actually think your preceding makes even the least bit of sense, then you
>
> overestimate your math skills. Simply interpret the equation. Of course no such definable endsegment exists because only dark endsegments proiduce the empty intersection.
>
> Regards, WM

"...overestimate your math skills." -WM Another Keeper!

∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }

OMG !!! True or false ? How to determine ???

WELL, could try math...

assume k is in the intersection.

but k is in E(1) to E(k), and k is not in E(k+1), E(k+2)...

SO any intersection of Endsegments that includes any E(k+1), or E(k+2)... is EMPTY

simplifying above;

∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)})

∩({E(X+1), E(X+2), E(X+3), ...})

So now we have a race between X and k...

Three cases;

X > k, X = k, and X < k

let X = k + a where a is the difference or offset

in all three cases there are E(k+a+1), or E(k+a+2), ..., which do not contain k

so in all cases the intersection is empty, as k is not in the intersection

∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }

Re: Natural numbers and vases III

<tclu3n$15jo$2@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108326&group=sci.math#108326

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: Sat, 6 Aug 2022 09:33:25 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tclu3n$15jo$2@gioia.aioe.org>
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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
<b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="38520"; 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 - Sat, 6 Aug 2022 14:33 UTC

On 8/6/2022 5:49 AM, WM wrote:
> 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.

Wrong. try using math instead of guessing.

>
> One of them would be enough!
>
> Regards, WM

Re: Natural numbers and vases III

<tclu6m$15jo$3@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108327&group=sci.math#108327

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: Sat, 6 Aug 2022 09:35:00 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tclu6m$15jo$3@gioia.aioe.org>
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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
<04139ba9-12a3-475f-8e90-84cfb53fa11bn@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="38520"; 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 - Sat, 6 Aug 2022 14:35 UTC

Re: Natural numbers and vases III

<bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108328&group=sci.math#108328

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1ba7:b0:31f:3732:ff1d with SMTP id bp39-20020a05622a1ba700b0031f3732ff1dmr9971076qtb.35.1659799666476;
Sat, 06 Aug 2022 08:27:46 -0700 (PDT)
X-Received: by 2002:aca:2219:0:b0:342:b399:754b with SMTP id
b25-20020aca2219000000b00342b399754bmr241472oic.1.1659799666209; Sat, 06 Aug
2022 08:27:46 -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 08:27:45 -0700 (PDT)
In-Reply-To: <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sat, 06 Aug 2022 15:27:46 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8295

by: William - Sat, 6 Aug 2022 15:27 UTC

On Saturday, August 6, 2022 at 7:49:27 AM UTC-3, WM wrote:
> 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.

Nope. 1, Each element of |N is "individually definable' and 2, ∩{E(k) : k ∈ ℕ} = { } It follows that the set of endsegments is a set
of "individually definable" endsegments with empty intersection

>... the way [the ability to be written down] is proved by [wrinting down], not by "proving" [that the element has the property (can be written donwn)]

Piffle. Let n be a natural number. Writing n down is only one method of showing that n has the property (can be written down)
> >
> > ... 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.

Piffle if you remove the *set* "Every definalbe endsegment", there is nothing left. What you can do is remove any *element* (or any finite subset of elements) of the *set* "Every definalbe endsegment"

--
William Hughes

Re: Natural numbers and vases III

<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108329&group=sci.math#108329

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:296:b0:31f:5e7:272c with SMTP id z22-20020a05622a029600b0031f05e7272cmr10329382qtw.146.1659800410112;
Sat, 06 Aug 2022 08:40:10 -0700 (PDT)
X-Received: by 2002:a05:6870:c598:b0:108:b7e2:ac8 with SMTP id
ba24-20020a056870c59800b00108b7e20ac8mr9021312oab.1.1659800409846; Sat, 06
Aug 2022 08:40:09 -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: Sat, 6 Aug 2022 08:40:09 -0700 (PDT)
In-Reply-To: <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sat, 06 Aug 2022 15:40:10 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6419

by: William - Sat, 6 Aug 2022 15:40 UTC

Re: Natural numbers and vases III

<1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108331&group=sci.math#108331

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1448:b0:341:e523:fd18 with SMTP id v8-20020a05622a144800b00341e523fd18mr9797545qtx.338.1659800744954;
Sat, 06 Aug 2022 08:45:44 -0700 (PDT)
X-Received: by 2002:a05:6830:6183:b0:616:a125:1f84 with SMTP id
cb3-20020a056830618300b00616a1251f84mr4252194otb.350.1659800744738; Sat, 06
Aug 2022 08:45:44 -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 08:45:44 -0700 (PDT)
In-Reply-To: <04139ba9-12a3-475f-8e90-84cfb53fa11bn@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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 06 Aug 2022 15:45:44 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6660

by: Gus Gassmann - Sat, 6 Aug 2022 15:45 UTC

Re: Natural numbers and vases III

<3cab2629-2fb5-4fe0-b632-8d7b67669f65n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108352&group=sci.math#108352

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:5d2:b0:31f:229d:441d with SMTP id d18-20020a05622a05d200b0031f229d441dmr10977708qtb.277.1659818743858;
Sat, 06 Aug 2022 13:45:43 -0700 (PDT)
X-Received: by 2002:a05:6870:61d4:b0:112:ddb:1adb with SMTP id
b20-20020a05687061d400b001120ddb1adbmr5841693oah.43.1659818743650; Sat, 06
Aug 2022 13:45:43 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 13:45:43 -0700 (PDT)
In-Reply-To: <bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:64d2:561b:4cfc:c8fb;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:64d2:561b:4cfc:c8fb
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> <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
<bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <3cab2629-2fb5-4fe0-b632-8d7b67669f65n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 20:45:43 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 8280

by: WM - Sat, 6 Aug 2022 20:45 UTC

William schrieb am Samstag, 6. August 2022 um 17:27:50 UTC+2:
> On Saturday, August 6, 2022 at 7:49:27 AM UTC-3, WM wrote:

> > > 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.
> Nope. 1, Each element of |N is "individually definable' and 2, ∩{E(k) : k ∈ ℕ} = { } It follows that the set of endsegments is a set
> of "individually definable" endsegments with empty intersection

All individually definable natnumbers index endsegments which can be omitted from the set of endsegments. The remainder does not contain any definable endsegment but has an empty intersection.

> >... the way [the ability to be written down] is proved by [wrinting down], not by "proving" [that the element has the property (can be written donwn)]
>
> Let n be a natural number. Writing n down is only one method of showing that n has the property (can be written down)

It is the only reliable way.
> > >
> > > ... 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.
> Piffle if you remove the *set* "Every definalbe endsegment", there is nothing left.

There is a lot left. Infinitely many endsegments which are required to get an empty intersection.

> What you can do is remove any *element* (or any finite subset of elements) of the *set* "Every definalbe endsegment"

I remove every definable ensegment and all its predecessors such that no definable endsegment remains. I remove, by induction, all endsegments that can be removed without changing the empty intersection. That means all definable endsegments are removed. Infinitely many undefinable endsegments are yielding an empty intersection.

Regards, WM

Re: Natural numbers and vases III

<babf9e59-d9b5-408f-829e-18c6e5d7eb07n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108353&group=sci.math#108353

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5c8c:0:b0:477:d19:1a44 with SMTP id o12-20020ad45c8c000000b004770d191a44mr10730292qvh.15.1659818751470;
Sat, 06 Aug 2022 13:45:51 -0700 (PDT)
X-Received: by 2002:a05:6830:a90:b0:636:db84:ed11 with SMTP id
n16-20020a0568300a9000b00636db84ed11mr187310otu.151.1659818751232; Sat, 06
Aug 2022 13:45:51 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 13:45:51 -0700 (PDT)
In-Reply-To: <c31c2266-9395-4877-bc2f-0b7c70b1f20cn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:64d2:561b:4cfc:c8fb;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:64d2:561b:4cfc:c8fb
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>
<c31c2266-9395-4877-bc2f-0b7c70b1f20cn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <babf9e59-d9b5-408f-829e-18c6e5d7eb07n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 20:45:51 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6694

by: WM - Sat, 6 Aug 2022 20:45 UTC

Re: Natural numbers and vases III

<e600ecba-5e38-40e0-a1e1-0f62be035093n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108354&group=sci.math#108354

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4726:b0:6b6:2239:f5f7 with SMTP id bs38-20020a05620a472600b006b62239f5f7mr9561547qkb.96.1659818755335;
Sat, 06 Aug 2022 13:45:55 -0700 (PDT)
X-Received: by 2002:a05:6870:338e:b0:f3:1a36:9485 with SMTP id
w14-20020a056870338e00b000f31a369485mr9138094oae.277.1659818755141; Sat, 06
Aug 2022 13:45:55 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 13:45:54 -0700 (PDT)
In-Reply-To: <tclo7u$3ruh7$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:64d2:561b:4cfc:c8fb;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:64d2:561b:4cfc:c8fb
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>
<tclo7u$3ruh7$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <e600ecba-5e38-40e0-a1e1-0f62be035093n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 20:45:55 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2561

by: WM - Sat, 6 Aug 2022 20:45 UTC

Re: Natural numbers and vases III

<2310ed98-640e-4b63-8001-06e898a4721dn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108355&group=sci.math#108355

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:30d:b0:6b9:2494:9913 with SMTP id s13-20020a05620a030d00b006b924949913mr4573514qkm.253.1659819012793;
Sat, 06 Aug 2022 13:50:12 -0700 (PDT)
X-Received: by 2002:aca:b60a:0:b0:342:894c:2277 with SMTP id
g10-20020acab60a000000b00342894c2277mr5476816oif.43.1659819012602; Sat, 06
Aug 2022 13:50:12 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 13:50:12 -0700 (PDT)
In-Reply-To: <1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:64d2:561b:4cfc:c8fb;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:64d2:561b:4cfc:c8fb
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <2310ed98-640e-4b63-8001-06e898a4721dn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 20:50:12 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6684

by: WM - Sat, 6 Aug 2022 20:50 UTC

Re: Natural numbers and vases III

<17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108357&group=sci.math#108357

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:27ce:b0:477:2f42:a199 with SMTP id ge14-20020a05621427ce00b004772f42a199mr10556495qvb.115.1659819681009;
Sat, 06 Aug 2022 14:01:21 -0700 (PDT)
X-Received: by 2002:a05:6808:aad:b0:342:9a85:882c with SMTP id
r13-20020a0568080aad00b003429a85882cmr7413967oij.80.1659819680724; Sat, 06
Aug 2022 14:01:20 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 14:01:20 -0700 (PDT)
In-Reply-To: <c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ec63:64d2:561b:4cfc:c8fb;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ec63:64d2:561b:4cfc:c8fb
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 06 Aug 2022 21:01:20 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7438

by: WM - Sat, 6 Aug 2022 21:01 UTC

William schrieb am Samstag, 6. August 2022 um 17:40:14 UTC+2:
> On Saturday, August 6, 2022 at 9:34:23 AM UTC-3, WM wrote:
> > William schrieb am Freitag, 5. August 2022 um 19:07:03 UTC+2:
> >
> > > We know that we cannot write down an infinite number of natural numbers.
> > One would be enough, namely one that changes the intersection
> Piffle. One is not "enough". You need an infinite subset to change the intersection.

Result: Every definable endsegment together with all its predecessors is not enough. Infinite subsets are not subsets of definable endsegments.

> You cannot write down each element of a infinite set, but you can know that each element has the property can be written down (independent of time and resources).

You can have the delusion to know that. But it is wrong. It is impossible to define more than can be defined by induction. By induction you can prove that all definable endsegments leave a set of endsegments having an empty intersection.

If you could define an endsegment or a set of endsegments {E(k) : k ∈ ℕ_def} which changes the intersection ∩{E(k) : k ∈ ℕ} = { } = ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}, you would do it. But you can't, since the empty intersection depends solely on the dark endsegments.

Regards, WM

Re: Natural numbers and vases III

<tcmmrb$1bhq$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108358&group=sci.math#108358

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: Sat, 6 Aug 2022 16:35:38 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcmmrb$1bhq$1@gioia.aioe.org>
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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
<b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
<bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com>
<3cab2629-2fb5-4fe0-b632-8d7b67669f65n@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="44602"; 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 - Sat, 6 Aug 2022 21:35 UTC

On 8/6/2022 3:45 PM, WM wrote:
> William schrieb am Samstag, 6. August 2022 um 17:27:50 UTC+2:
>> On Saturday, August 6, 2022 at 7:49:27 AM UTC-3, WM wrote:
>
>>>> 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.
>> Nope. 1, Each element of |N is "individually definable' and 2, ∩{E(k) : k ∈ ℕ} = { } It follows that the set of endsegments is a set
>> of "individually definable" endsegments with empty intersection
>
> All individually definable natnumbers index endsegments which can be omitted from the set of endsegments. The remainder does not contain any definable endsegment but has an empty intersection.

good Golly! you gosta simplify! I mean cut the crap out, thusly;

"All individually definable natnumbers index endsegments which can be omitted from the set of endsegments." => natnumbers index endsegments

"The remainder does not contain any definable endsegment but has an empty intersection." => {}

nothing else there.

>
>>> ... the way [the ability to be written down] is proved by [wrinting down], not by "proving" [that the element has the property (can be written donwn)]
>>
>> Let n be a natural number. Writing n down is only one method of showing that n has the property (can be written down)
>
> It is the only reliable way.

what about using your definition of "defined" using raps, and taps, beeps, flashs of light, or a colors of the rainbow ?
Quackings from a duck should work just fine too.

>>>>
>>>> ... 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.
>> Piffle if you remove the *set* "Every definalbe endsegment", there is nothing left.
>
> There is a lot left. Infinitely many endsegments which are required to get an empty intersection.

there is nothing left.

>
>> What you can do is remove any *element* (or any finite subset of elements) of the *set* "Every definalbe endsegment"
>
> I remove every definable ensegment and all its predecessors such that no definable endsegment remains.

Why dont you just remove everything ? why limit yourself ?

> I remove, by induction,

you deny induction, you dont know what induction is. You are a single line Math dude and no more.

>
> Regards, WM

Failure at math.

Re: Natural numbers and vases III

<tcmn48$1ebn$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108360&group=sci.math#108360

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: Sat, 6 Aug 2022 16:40:23 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcmn48$1ebn$1@gioia.aioe.org>
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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
<04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com>
<17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="47479"; 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 - Sat, 6 Aug 2022 21:40 UTC

On 8/6/2022 4:01 PM, WM wrote:
> William schrieb am Samstag, 6. August 2022 um 17:40:14 UTC+2:
>> On Saturday, August 6, 2022 at 9:34:23 AM UTC-3, WM wrote:
>>> William schrieb am Freitag, 5. August 2022 um 19:07:03 UTC+2:
>>>
>>>> We know that we cannot write down an infinite number of natural numbers.
>>> One would be enough, namely one that changes the intersection
>> Piffle. One is not "enough". You need an infinite subset to change the intersection.
>
> Result: Every definable endsegment together with all its predecessors is not enough. Infinite subsets are not subsets of definable endsegments.

that is 2 lies.

>
>> You cannot write down each element of a infinite set, but you can know that each element has the property can be written down (independent of time and resources).
>
> You can have the delusion to know that. But it is wrong. It is impossible to define more than can be defined by induction. By induction you can prove that all definable endsegments leave a set of endsegments having an empty intersection.

its wrong since you use your "definable" misdirector term.

>
> If you could define an endsegment or a set of endsegments {E(k) : k ∈ ℕ_def} which changes the intersection ∩{E(k) : k ∈ ℕ} = { } = ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}, you would do it. But you can't, since the empty intersection depends solely on the dark endsegments.

gad, you are way out there buddy! spaced kaddett
its your imagination and ego, not math, that got you into your illogical hole, and you cant get out.

>
> Regards, WM

Re: Natural numbers and vases III

<tcmnav$1gk6$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108361&group=sci.math#108361

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: Sat, 6 Aug 2022 16:43:58 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcmnav$1gk6$1@gioia.aioe.org>
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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com>
<04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com>
<2310ed98-640e-4b63-8001-06e898a4721dn@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="49798"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US

by: Sergio - Sat, 6 Aug 2022 21:43 UTC

Re: Natural numbers and vases III

<tcmq0n$4j91$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108366&group=sci.math#108366

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 18:29:35 -0400
Organization: Peripheral Visions
Lines: 39
Message-ID: <tcmq0n$4j91$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> <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com> <bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com> <3cab2629-2fb5-4fe0-b632-8d7b67669f65n@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 22:29:43 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="c8f862875b870cba5f7eab81c2efcb94";
logging-data="150817"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18/qHdM+KzIrH+ibdaMQuIhKE8fiaMWJ24="
Cancel-Lock: sha1:43r3jshLOlDatBzJpaFScxfWw28=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb

by: FromTheRafters - Sat, 6 Aug 2022 22:29 UTC

WM presented the following explanation :
> William schrieb am Samstag, 6. August 2022 um 17:27:50 UTC+2:
>> On Saturday, August 6, 2022 at 7:49:27 AM UTC-3, WM wrote:
>
>>>> 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.
>> Nope. 1, Each element of |N is "individually definable' and 2, ∩{E(k) : k ∈
>> ℕ} = { } It follows that the set of endsegments is a set of "individually
>> definable" endsegments with empty intersection
>
> All individually definable natnumbers index endsegments which can be omitted
> from the set of endsegments. The remainder does not contain any definable
> endsegment but has an empty intersection.
>
>>> ... the way [the ability to be written down] is proved by [wrinting down],
>>> not by "proving" [that the element has the property (can be written donwn)]
>>
>> Let n be a natural number. Writing n down is only one method of showing that
>> n has the property (can be written down)
>
> It is the only reliable way.
>>>>
>>>> ... 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.
>> Piffle if you remove the *set* "Every definalbe endsegment", there is
>> nothing left.
>
> There is a lot left. Infinitely many endsegments which are required to get an
> empty intersection.

All you need is no last element.

Re: Natural numbers and vases III

<tcmq6s$4kuo$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108367&group=sci.math#108367

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 18:32:52 -0400
Organization: Peripheral Visions
Lines: 14
Message-ID: <tcmq6s$4kuo$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> <a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com> <c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
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 22:33:00 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="c8f862875b870cba5f7eab81c2efcb94";
logging-data="152536"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19265TIWpLt8a8ksTinka3L1OLhTktvAyc="
Cancel-Lock: sha1:0L6Xg+J/nSQdb6DnfcZ4rmvFz1o=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Sat, 6 Aug 2022 22:32 UTC

Re: Natural numbers and vases III

<7eaf405b-e0dd-4dac-a667-f3ea2918e80dn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108368&group=sci.math#108368

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1646:b0:33c:cecc:96e4 with SMTP id y6-20020a05622a164600b0033ccecc96e4mr11304904qtj.350.1659825208913;
Sat, 06 Aug 2022 15:33:28 -0700 (PDT)
X-Received: by 2002:a05:6870:2483:b0:ed:f721:2734 with SMTP id
s3-20020a056870248300b000edf7212734mr5715566oaq.242.1659825208676; Sat, 06
Aug 2022 15:33:28 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 15:33:28 -0700 (PDT)
In-Reply-To: <3cab2629-2fb5-4fe0-b632-8d7b67669f65n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
<bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com> <3cab2629-2fb5-4fe0-b632-8d7b67669f65n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <7eaf405b-e0dd-4dac-a667-f3ea2918e80dn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sat, 06 Aug 2022 22:33:28 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6302

by: William - Sat, 6 Aug 2022 22:33 UTC

Re: Natural numbers and vases III

<tcmqki$4odv$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108369&group=sci.math#108369

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 18:40:10 -0400
Organization: Peripheral Visions
Lines: 16
Message-ID: <tcmqki$4odv$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <tclo7u$3ruh7$1@dont-email.me> <e600ecba-5e38-40e0-a1e1-0f62be035093n@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 22:40:18 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="c8f862875b870cba5f7eab81c2efcb94";
logging-data="156095"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18cDXwgMuYXzR3ug7k3TMq8oc04jF2zBCk="
Cancel-Lock: sha1:RVJ74FJJ4c41xeRZczSWvVYNhg4=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb

by: FromTheRafters - Sat, 6 Aug 2022 22:40 UTC

Re: Natural numbers and vases III

<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108370&group=sci.math#108370

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:301d:b0:476:a151:1d7c with SMTP id ke29-20020a056214301d00b00476a1511d7cmr10875198qvb.121.1659826116118;
Sat, 06 Aug 2022 15:48:36 -0700 (PDT)
X-Received: by 2002:a05:6808:1b85:b0:33a:7a2b:3ff7 with SMTP id
cj5-20020a0568081b8500b0033a7a2b3ff7mr5492213oib.152.1659826115910; Sat, 06
Aug 2022 15:48:35 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.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 15:48:35 -0700 (PDT)
In-Reply-To: <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sat, 06 Aug 2022 22:48:36 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6736

by: William - Sat, 6 Aug 2022 22:48 UTC

Re: Natural numbers and vases III

<tcn9r4$1dak$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108385&group=sci.math#108385

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: Sat, 6 Aug 2022 21:59:47 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcn9r4$1dak$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<tclo7u$3ruh7$1@dont-email.me>
<e600ecba-5e38-40e0-a1e1-0f62be035093n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="46420"; 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 - Sun, 7 Aug 2022 02:59 UTC

Re: Natural numbers and vases III

<tcna93$1gqr$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108386&group=sci.math#108386

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: Sat, 6 Aug 2022 22:07:14 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcna93$1gqr$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<c31c2266-9395-4877-bc2f-0b7c70b1f20cn@googlegroups.com>
<babf9e59-d9b5-408f-829e-18c6e5d7eb07n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="50011"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.12.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US

by: Sergio - Sun, 7 Aug 2022 03:07 UTC

On 8/6/2022 3:45 PM, WM wrote:
> Gus Gassmann schrieb am Samstag, 6. August 2022 um 16:20:28 UTC+2:
>> On Saturday, 6 August 2022 at 08:49:16 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Samstag, 6. August 2022 um 13:43:21 UTC+2:
>> [...]
>>>> And you have no clue about induction.
>>> There is no clue necessary if one knows a bit of mathematics.
>> Anyone who thinks that induction can only define a finite number of objects
>
> All number defined by induction index endsegments which can be omitted from the set of endsegments. The remainder does not contain any definable endsegment but has an empty intersection.

you are just not thinking right. Press your RESET button.

Since you refuse to use equations, what do you specifically mean by:

them index endsegments (endsegments are indexed by the natural numbers, so WTF is this?)
can be omitted (is this an operation on a set ?)
set of endsegments ( all endsegments, partial set, any set ??)
The remainder (of what ? )
does not contain ( do you mean ELEMENT OF A SET ?)
definable endsegment (that is nonsense on its face)

Any Answers ?

No?

I hope you are studding your algebra

>
> Regards, WM

Re: Natural numbers and vases III

<21c8f979-eb17-4a26-8eec-c7a89c7efcb1n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108398&group=sci.math#108398

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:2b86:b0:6b9:4a51:98f6 with SMTP id dz6-20020a05620a2b8600b006b94a5198f6mr789063qkb.36.1659875445500;
Sun, 07 Aug 2022 05:30:45 -0700 (PDT)
X-Received: by 2002:a9d:1b64:0:b0:636:916d:d45a with SMTP id
l91-20020a9d1b64000000b00636916dd45amr5204810otl.75.1659875445258; Sun, 07
Aug 2022 05:30:45 -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: Sun, 7 Aug 2022 05:30:45 -0700 (PDT)
In-Reply-To: <7eaf405b-e0dd-4dac-a667-f3ea2918e80dn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ecaa:20cb:2fbc:3782:97d2;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ecaa:20cb:2fbc:3782:97d2
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> <b3b7c880-2e71-4c8e-87d3-c0e2ae9ba0ecn@googlegroups.com>
<bd2e950a-c765-48a5-90b9-724c690b5fb5n@googlegroups.com> <3cab2629-2fb5-4fe0-b632-8d7b67669f65n@googlegroups.com>
<7eaf405b-e0dd-4dac-a667-f3ea2918e80dn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <21c8f979-eb17-4a26-8eec-c7a89c7efcb1n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 07 Aug 2022 12:30:45 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 6626

by: WM - Sun, 7 Aug 2022 12:30 UTC

Re: Natural numbers and vases III

<da0045ff-6935-4376-afb9-1fcac24edc31n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108399&group=sci.math#108399

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:2909:b0:6b6:a94:a988 with SMTP id m9-20020a05620a290900b006b60a94a988mr11321234qkp.350.1659875593154;
Sun, 07 Aug 2022 05:33:13 -0700 (PDT)
X-Received: by 2002:a05:6870:f221:b0:113:929e:9f71 with SMTP id
t33-20020a056870f22100b00113929e9f71mr1816563oao.7.1659875592942; Sun, 07 Aug
2022 05:33:12 -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: Sun, 7 Aug 2022 05:33:12 -0700 (PDT)
In-Reply-To: <tcmqki$4odv$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ecaa:20cb:2fbc:3782:97d2;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ecaa:20cb:2fbc:3782:97d2
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <tclo7u$3ruh7$1@dont-email.me>
<e600ecba-5e38-40e0-a1e1-0f62be035093n@googlegroups.com> <tcmqki$4odv$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <da0045ff-6935-4376-afb9-1fcac24edc31n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 07 Aug 2022 12:33:13 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2573

by: WM - Sun, 7 Aug 2022 12:33 UTC

Re: Natural numbers and vases III

<9deb4284-0692-4db3-91de-195376fc01d6n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108400&group=sci.math#108400

copy link Newsgroups: sci.math

X-Received: by 2002:a37:43d4:0:b0:6b8:e3ba:ddfc with SMTP id q203-20020a3743d4000000b006b8e3baddfcmr10883213qka.192.1659875737289;
Sun, 07 Aug 2022 05:35:37 -0700 (PDT)
X-Received: by 2002:a05:6808:aad:b0:342:9a85:882c with SMTP id
r13-20020a0568080aad00b003429a85882cmr8235690oij.80.1659875737079; Sun, 07
Aug 2022 05:35:37 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!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: Sun, 7 Aug 2022 05:35:36 -0700 (PDT)
In-Reply-To: <2310ed98-640e-4b63-8001-06e898a4721dn@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>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<1c9ba0a9-289d-4dc5-86fb-1ce7722d48e1n@googlegroups.com> <2310ed98-640e-4b63-8001-06e898a4721dn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <9deb4284-0692-4db3-91de-195376fc01d6n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sun, 07 Aug 2022 12:35:37 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7195

by: Gus Gassmann - Sun, 7 Aug 2022 12:35 UTC

Re: Natural numbers and vases III

<b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108401&group=sci.math#108401

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4542:b0:6b3:7c51:6177 with SMTP id u2-20020a05620a454200b006b37c516177mr11037842qkp.306.1659875889119;
Sun, 07 Aug 2022 05:38:09 -0700 (PDT)
X-Received: by 2002:a05:6830:6613:b0:61c:acf8:8e41 with SMTP id
cp19-20020a056830661300b0061cacf88e41mr5110880otb.298.1659875888911; Sun, 07
Aug 2022 05:38:08 -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: Sun, 7 Aug 2022 05:38:08 -0700 (PDT)
In-Reply-To: <53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:ecaa:20cb:2fbc:3782:97d2;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:ecaa:20cb:2fbc:3782:97d2
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
<5d2757f0-0ee0-4e17-bc43-ea9bac4d0d13n@googlegroups.com> <b5fc594a-df20-446a-9e71-25e09bfe6d83n@googlegroups.com>
<a7412fa0-6dec-4d41-a828-38ff267235f5n@googlegroups.com> <c0adf15c-b4a4-40e9-9d2b-eeb68cdcaca8n@googlegroups.com>
<4c6f2df7-34e5-4325-b4b6-682a0eaebed9n@googlegroups.com> <e9b8774e-c95b-47d4-869c-ef45d9938cacn@googlegroups.com>
<b251bc23-5ff5-4f6a-8c06-77e8d7a3af6bn@googlegroups.com> <40af57e3-35e1-42ba-be98-9a214488426dn@googlegroups.com>
<816dccd1-dff2-4be9-ba22-acfe6832bd70n@googlegroups.com> <ba929c70-156b-4950-a9d0-5f981636eaefn@googlegroups.com>
<a67fac43-8ea1-4f3b-8a81-a2ab211190fen@googlegroups.com> <04139ba9-12a3-475f-8e90-84cfb53fa11bn@googlegroups.com>
<c620d235-23f6-4074-93e7-7cfdbfa2ff61n@googlegroups.com> <17601f67-f109-4788-b365-fdd4d07e7f33n@googlegroups.com>
<53b91224-15b1-4235-adea-777b31a9b3ddn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <b58045bf-3c51-448d-8b9a-d013425e7190n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 07 Aug 2022 12:38:09 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7532

by: WM - Sun, 7 Aug 2022 12:38 UTC

William schrieb am Sonntag, 7. August 2022 um 00:48:39 UTC+2:
> On Saturday, August 6, 2022 at 6:01:26 PM UTC-3, WM wrote:
> >...Infinite subsets are not subsets of definable endsegments.
>
> Piffle. Let S be any subset of endsegments. Each element of S is definable. So S is a "subset of definable endsegments"
> > > You cannot write down each element of a infinite set, but you can know that each element has the property can be written down (independent of time and resources).
> > You can have the delusion to know that. But it is wrong.
> Nope. Induction works for each element of the Infinite set |N.

If it did, then no endsegment would remain after each and all endsegments subject to induction had been omitted.
>
> >... all definable endsegments leave[s] a set of endsegments having an empty intersection.
>
> "all definable endsegments" is a set. Removing this set leaves nothing.
>
Induction works for each element, not for the set. Each definable endsegment satisfies
∀k ∈ ℕ-def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀.
It cannot cause an empty intersection but can be removed from the set of all endsegments without changing the intersection

∩{E(k) : k > n, k ∈ ℕ, n ∈ ℕ_ind} = { } .

Regards, WM

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