Message-ID:

<Tazman> damn my office is cold. <Tazman> need a hot secretary to warm it up. -- Seen on #Linux

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

Re: Natural numbers and vases III

<6739be9c-db90-4d1b-ba73-285f90fd9917n@googlegroups.com>

https://www.novabbs.com/tech/article-flat.php?id=107714&group=sci.math#107714

X-Received: by 2002:a05:622a:1a10:b0:31f:16be:c2bc with SMTP id f16-20020a05622a1a1000b0031f16bec2bcmr7754005qtb.175.1659192670941;
Sat, 30 Jul 2022 07:51:10 -0700 (PDT)
X-Received: by 2002:aca:b744:0:b0:32f:4c19:cec1 with SMTP id
h65-20020acab744000000b0032f4c19cec1mr3687591oif.43.1659192670717; Sat, 30
Jul 2022 07:51:10 -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, 30 Jul 2022 07:51:10 -0700 (PDT)
In-Reply-To: <tc3bek$3s4hn$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:561d:dcc3:a1cb:896:1795;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:561d:dcc3:a1cb:896:1795
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com> <e2926fa8-0e00-460f-9661-9bffed3051edn@googlegroups.com>
<tc0rbq$3hbpo$1@dont-email.me> <6a2634de-3907-423b-99ca-096022535e0dn@googlegroups.com>
<7111b4a8-64b2-4f3c-a295-678c9c4f090an@googlegroups.com> <04b60c68-1dc3-44c0-816f-7ce1822771ebn@googlegroups.com>
<tc3bek$3s4hn$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <6739be9c-db90-4d1b-ba73-285f90fd9917n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 30 Jul 2022 14:51:10 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 4282

by: WM - Sat, 30 Jul 2022 14:51 UTC

FromTheRafters schrieb am Samstag, 30. Juli 2022 um 15:24:45 UTC+2:
> WM brought next idea :
> > Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 17:49:01 UTC+2:
> >> On Friday, July 29, 2022 at 5:17:19 PM UTC+2, WM wrote:
> >>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >>>> WM laid this down on his screen :
> >>>>> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> >>>>>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
> >>>>>>>
> >>>>>>> We still have that a "final state" exists [...]
> >>>>>>>
> >>>>>> You are talking nonsense. And you know it, asshole!
> >>>>>>
> >>>>>> The limit of a sequence is not a "final state" (of what?!).
> >>>>>>
> >>>>> The completion of a set is the final state.
> >>>>>
> >>>> A set is not a process, though it can be a function.
> >>>>
> >>> In ZFC everything is a set. Processes can be decribed by mathematics.
> >>> Mathematics is based on ZFC. Conclusion: Processes [can be] described as
> >>> sets.
> >>
> >> Did ANYONE claim otherwise, Mückenheim? :-)
> >
> > Some fools claim that infinite processes, so-called supertasks, do not belong
> > to set theory although its main advantage is the description of the actions
> > of infinite sets and of super tasks, for instance enumerating the farctions.
> If you want time and steps to be part of your mathematics, you must
> include them.

Steps and the legitimate right to know every indexed term are included by the definition of the natural numbers. They arise from Peano's n ==> n+1..

> A bijection takes no time at all, and there are no steps
> or supertasks involved.

The definition of the bijection is fast, but there are steps 1, 2, 3, ..., k to every definable number k:
∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ ..
There are no steps however to any endsegment which makes the intersection of endsegments less than infinite or even ∩{E(k) : k ∈ ℕ} = { }.

Regards, WM

Re: Natural numbers and vases III

<d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107715&group=sci.math#107715

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:4690:b0:6b5:dbd5:e30 with SMTP id bq16-20020a05620a469000b006b5dbd50e30mr6503759qkb.35.1659193080897;
Sat, 30 Jul 2022 07:58:00 -0700 (PDT)
X-Received: by 2002:aca:1103:0:b0:33a:c295:f483 with SMTP id
3-20020aca1103000000b0033ac295f483mr4089705oir.80.1659193080679; Sat, 30 Jul
2022 07:58:00 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sat, 30 Jul 2022 07:58:00 -0700 (PDT)
In-Reply-To: <55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:561d:dcc3:a1cb:896:1795;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:561d:dcc3:a1cb:896:1795
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 30 Jul 2022 14:58:00 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6013

by: WM - Sat, 30 Jul 2022 14:58 UTC

William schrieb am Samstag, 30. Juli 2022 um 16:50:51 UTC+2:
> On Saturday, July 30, 2022 at 9:19:32 AM UTC-3, WM wrote:
>
> > The final state like omega does not change in actual infinity. It canot be reached
> By "can be reached " you mean "is an element or subset of the state at a step of a stepwise process".

Here you have an example: There are steps 1, 2, 3, ..., k to every definable number k such that:
∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ ..
There are no steps however to any endsegment which makes the intersection of endsegments less than infinite or even ∩{E(k) : k ∈ ℕ} = { }.

This is an easily understandable difference, isn't it?

>As you note, a "final state" exists.
Yes, in case of endsegments it is the empty intersection.

> > because its predecessors are dark.

> Piffle. |N is a Peano set and does not contain "dark elements". The reason a "final state cannot" be reached by a stepwise process is that the state changes at every step and there is no last step,

Here the last step has been done: ∩{E(k) : k ∈ ℕ} = { }.

> The reason has nothing to do with "dark elements". Note, the fact that each *element* of |N has the property "can be reached" does not mean the *set* |N has the property "can be reached".

So the set is far beyond each definable element. What causes the difference?
Here you see the difference. For each definable element we get
∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
but for the set we get
∩{E(k) : k ∈ ℕ} = { }.

Regards, WM

Re: Natural numbers and vases III

<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107716&group=sci.math#107716

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:5a4d:0:b0:31f:3803:be3 with SMTP id o13-20020ac85a4d000000b0031f38030be3mr7513035qta.518.1659194815097;
Sat, 30 Jul 2022 08:26:55 -0700 (PDT)
X-Received: by 2002:a05:6808:1b85:b0:33a:7a2b:3ff7 with SMTP id
cj5-20020a0568081b8500b0033a7a2b3ff7mr3566326oib.152.1659194814876; Sat, 30
Jul 2022 08:26:54 -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, 30 Jul 2022 08:26:54 -0700 (PDT)
In-Reply-To: <d94da021-4874-4920-b101-06cf2a697753n@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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sat, 30 Jul 2022 15:26:55 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5170

by: William - Sat, 30 Jul 2022 15:26 UTC

On Saturday, July 30, 2022 at 11:58:06 AM UTC-3, WM wrote:
> William schrieb am Samstag, 30. Juli 2022 um 16:50:51 UTC+2:

> > Piffle. |N is a Peano set and does not contain "dark elements". The reason a "final state cannot" be reached by a stepwise process is that the state changes at every step and there is no last step,
> Here the last step has been done: ∩{E(k) : k ∈ ℕ} = { }.

Nope, There is no last k, so there is no last step. ("there is no step that has not been done" does not imply "there is a last step done"). Note ∩{E(k) : k ∈ ℕ} is not the state of a stepwise process.

> ... What causes the difference?

The fact that each *element* of |N is contained in a finite subset of |N, but the *set* |N is not contained in a finite subset of |N.

--
William Hughes

Re: Natural numbers and vases III

<808e0b9f-9ea0-4b84-bd29-ca6acf8c656an@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107719&group=sci.math#107719

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:270e:b0:6b4:8425:d03c with SMTP id b14-20020a05620a270e00b006b48425d03cmr6786877qkp.732.1659201290560;
Sat, 30 Jul 2022 10:14:50 -0700 (PDT)
X-Received: by 2002:a05:6808:169e:b0:331:522a:4521 with SMTP id
bb30-20020a056808169e00b00331522a4521mr3810465oib.293.1659201290294; Sat, 30
Jul 2022 10:14:50 -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, 30 Jul 2022 10:14:50 -0700 (PDT)
In-Reply-To: <04b60c68-1dc3-44c0-816f-7ce1822771ebn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.196.61; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.196.61
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com> <e2926fa8-0e00-460f-9661-9bffed3051edn@googlegroups.com>
<tc0rbq$3hbpo$1@dont-email.me> <6a2634de-3907-423b-99ca-096022535e0dn@googlegroups.com>
<7111b4a8-64b2-4f3c-a295-678c9c4f090an@googlegroups.com> <04b60c68-1dc3-44c0-816f-7ce1822771ebn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <808e0b9f-9ea0-4b84-bd29-ca6acf8c656an@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sat, 30 Jul 2022 17:14:50 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2661

by: Fritz Feldhase - Sat, 30 Jul 2022 17:14 UTC

Re: Natural numbers and vases III

<91e4d6a2-a525-42c3-b019-d1bd2d1df896n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107720&group=sci.math#107720

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:7c44:0:b0:31f:3dc4:25db with SMTP id o4-20020ac87c44000000b0031f3dc425dbmr7785612qtv.612.1659201644445;
Sat, 30 Jul 2022 10:20:44 -0700 (PDT)
X-Received: by 2002:a05:6870:a78f:b0:101:d05b:fa3f with SMTP id
x15-20020a056870a78f00b00101d05bfa3fmr4116899oao.221.1659201640853; Sat, 30
Jul 2022 10:20:40 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sat, 30 Jul 2022 10:20:40 -0700 (PDT)
In-Reply-To: <2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.196.61; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.196.61
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <91e4d6a2-a525-42c3-b019-d1bd2d1df896n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sat, 30 Jul 2022 17:20:44 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 4742

by: Fritz Feldhase - Sat, 30 Jul 2022 17:20 UTC

Re: Natural numbers and vases III

<e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107721&group=sci.math#107721

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:194a:b0:473:75f5:ec8d with SMTP id q10-20020a056214194a00b0047375f5ec8dmr7961484qvk.130.1659201816020;
Sat, 30 Jul 2022 10:23:36 -0700 (PDT)
X-Received: by 2002:a05:6830:1e98:b0:61c:8438:5aaa with SMTP id
n24-20020a0568301e9800b0061c84385aaamr3562646otr.1.1659201815737; Sat, 30 Jul
2022 10:23:35 -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, 30 Jul 2022 10:23:35 -0700 (PDT)
In-Reply-To: <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.196.61; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.196.61
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sat, 30 Jul 2022 17:23:36 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 4138

by: Fritz Feldhase - Sat, 30 Jul 2022 17:23 UTC

Re: Natural numbers and vases III

<tc3pps$tpg$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107722&group=sci.math#107722

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, 30 Jul 2022 12:29:29 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tc3pps$tpg$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<e2926fa8-0e00-460f-9661-9bffed3051edn@googlegroups.com>
<tc0rbq$3hbpo$1@dont-email.me>
<6a2634de-3907-423b-99ca-096022535e0dn@googlegroups.com>
<7111b4a8-64b2-4f3c-a295-678c9c4f090an@googlegroups.com>
<04b60c68-1dc3-44c0-816f-7ce1822771ebn@googlegroups.com>
<tc3bek$3s4hn$1@dont-email.me>
<6739be9c-db90-4d1b-ba73-285f90fd9917n@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="30512"; 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/91.11.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US

by: Sergio - Sat, 30 Jul 2022 17:29 UTC

On 7/30/2022 9:51 AM, WM wrote:
> FromTheRafters schrieb am Samstag, 30. Juli 2022 um 15:24:45 UTC+2:
>> WM brought next idea :
>>> Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 17:49:01 UTC+2:
>>>> On Friday, July 29, 2022 at 5:17:19 PM UTC+2, WM wrote:
>>>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>>>>>> WM laid this down on his screen :
>>>>>>> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
>>>>>>>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>>>>>>>>>
>>>>>>>>> We still have that a "final state" exists [...]
>>>>>>>>>
>>>>>>>> You are talking nonsense. And you know it, asshole!
>>>>>>>>
>>>>>>>> The limit of a sequence is not a "final state" (of what?!).
>>>>>>>>
>>>>>>> The completion of a set is the final state.
>>>>>>>
>>>>>> A set is not a process, though it can be a function.
>>>>>>
>>>>> In ZFC everything is a set. Processes can be decribed by mathematics.
>>>>> Mathematics is based on ZFC. Conclusion: Processes [can be] described as
>>>>> sets.
>>>>
>>>> Did ANYONE claim otherwise, Mückenheim? :-)
>>>
>>> Some fools claim that infinite processes, so-called supertasks, do not belong
>>> to set theory although its main advantage is the description of the actions
>>> of infinite sets and of super tasks, for instance enumerating the farctions.
>> If you want time and steps to be part of your mathematics, you must
>> include them.
>
> Steps and the legitimate right to know every indexed term are included by the definition of the natural numbers. They arise from Peano's n ==> n+1.

you have not defined your "steps" in terms of math.

>
>> A bijection takes no time at all, and there are no steps
>> or supertasks involved.
>
> The definition of the bijection is fast, but there are steps 1, 2, 3, ..., k to every definable number k:
> ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ .

no, the equation says nothing about steps at all.

Besides, it is a very trivial equation.

> There are no steps however to any endsegment which makes the intersection of endsegments

the intersection of all endsegments is not an endsegment, so there is no way to step there, Why ? you did an operator ∩ called "intersection".

> less than infinite or even ∩{E(k) : k ∈ ℕ} = { }.

learn some math!

>
> Regards, WM
>

Re: Natural numbers and vases III

<78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107737&group=sci.math#107737

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5dea:0:b0:476:6a9e:b5ea with SMTP id jn10-20020ad45dea000000b004766a9eb5eamr1207076qvb.122.1659211355472;
Sat, 30 Jul 2022 13:02:35 -0700 (PDT)
X-Received: by 2002:a05:6808:13cc:b0:33a:a984:4c34 with SMTP id
d12-20020a05680813cc00b0033aa9844c34mr4309311oiw.1.1659211355181; Sat, 30 Jul
2022 13:02:35 -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, 30 Jul 2022 13:02:34 -0700 (PDT)
In-Reply-To: <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.125.241; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.125.241
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 30 Jul 2022 20:02:35 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 4417

by: Gus Gassmann - Sat, 30 Jul 2022 20:02 UTC

Re: Natural numbers and vases III

<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107745&group=sci.math#107745

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 30 Jul 2022 21:21:53 -0400
Organization: A noiseless patient Spider
Lines: 49
Message-ID: <961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com>
<e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net>
<bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: reader01.eternal-september.org; posting-host="7490eb61bb5c3bcd2fe90c4a5fa39fe9";
logging-data="125387"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19wVoxOTzm2br3jP7teNsvjicaPUq5Ljc4="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.11.0
Cancel-Lock: sha1:uOZYcaZL1X/c1Hlwxw/pFAjtaok=
In-Reply-To: <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
Content-Language: en-US

by: Jim Burns - Sun, 31 Jul 2022 01:21 UTC

On 7/30/2022 8:31 AM, WM wrote:
> Jim Burns schrieb
> am Freitag, 29. Juli 2022 um 18:55:08 UTC+2:

>> WM-dark numbers, end segments, fractions
>> can be hypothetically added to a WM-incomplete
>> subset to produce a WM-complete set.
>
> Very good!
>
>> the dark remainder can match itself,
>
> No.

Typically, claims in the definition are
easy to grant acceptance.

Typically, we know what we are talking about.

And,
if Alfred and Betty define naturals differently,
the one's conclusions may not apply to the other's,
and the other's may not apply to the one's.
There might not be common ground to dispute.

Here, your Alfred and my Betty have no common
ground to dispute. Your things which cannot match
themselves are not things which we are talking
about. Your conclusions, however well- or badly-
justified they are, are not about what we are
talking about. Go ahead and call them
"natural numbers", doing so won't change a thing.

>> WM-completeness requires elements which
>> _cannot_ match themselves.
>
> Yes.

Consider the Pythagorean theorem.
There is a triangle ABC such that
|AB|² ≠ |AC|² + |BC|²

ABC is not a right triangle.
Does it disprove the theorem?

If we can take someone else's theorem or other
claim and alter _what they are talking about_
then nothing can make any sense.

Re: Natural numbers and vases III

<664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107767&group=sci.math#107767

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:3012:b0:474:3d5a:6cd0 with SMTP id ke18-20020a056214301200b004743d5a6cd0mr9670673qvb.121.1659266396171;
Sun, 31 Jul 2022 04:19:56 -0700 (PDT)
X-Received: by 2002:a05:6870:65ab:b0:10e:7c08:9de7 with SMTP id
fp43-20020a05687065ab00b0010e7c089de7mr4977015oab.169.1659266395893; Sun, 31
Jul 2022 04:19:55 -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: Sun, 31 Jul 2022 04:19:55 -0700 (PDT)
In-Reply-To: <2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:563f:50ae:104f:a186:1f2a;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:563f:50ae:104f:a186:1f2a
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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 31 Jul 2022 11:19:56 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5717

by: WM - Sun, 31 Jul 2022 11:19 UTC

William schrieb am Samstag, 30. Juli 2022 um 17:26:59 UTC+2:
> On Saturday, July 30, 2022 at 11:58:06 AM UTC-3, WM wrote:
> > William schrieb am Samstag, 30. Juli 2022 um 16:50:51 UTC+2:
>
> > > Piffle. |N is a Peano set and does not contain "dark elements". The reason a "final state cannot" be reached by a stepwise process is that the state changes at every step and there is no last step,
> > Here the last step has been done: ∩{E(k) : k ∈ ℕ} = { }.
> Nope, There is no last k, so there is no last step. ("there is no step that has not been done" does not imply "there is a last step done"). Note ∩{E(k) : k ∈ ℕ} is not the state of a stepwise process..

It is the state where _all_ endsegments have been intersected --- you agree: all and nothing else. If there are all in a linear process or sequence, but no last exists or can be determined, then there is a subset of elements which cannot be ordered or distinguished. Why? Because they are dark.
>
> > ... What causes the difference?
>
> The fact that each *element* of |N is contained in a finite subset of |N, but the *set* |N is not contained in a finite subset of |N.

"The infinite set" is all its elements, isn't it?

Regards, WM

Re: Natural numbers and vases III

<16e00901-5498-4c37-8065-15bd37e3c901n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107768&group=sci.math#107768

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:c62:b0:474:3b6f:cb6 with SMTP id t2-20020a0562140c6200b004743b6f0cb6mr9967552qvj.126.1659268953346;
Sun, 31 Jul 2022 05:02:33 -0700 (PDT)
X-Received: by 2002:a05:6870:2483:b0:ed:f721:2734 with SMTP id
s3-20020a056870248300b000edf7212734mr5368524oaq.242.1659268953073; Sun, 31
Jul 2022 05:02:33 -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: Sun, 31 Jul 2022 05:02:32 -0700 (PDT)
In-Reply-To: <91e4d6a2-a525-42c3-b019-d1bd2d1df896n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:563f:50ae:104f:a186:1f2a;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:563f:50ae:104f:a186:1f2a
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> <91e4d6a2-a525-42c3-b019-d1bd2d1df896n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <16e00901-5498-4c37-8065-15bd37e3c901n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 31 Jul 2022 12:02:33 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5051

by: WM - Sun, 31 Jul 2022 12:02 UTC

Re: Natural numbers and vases III

<d86f0df8-3f98-48a5-88b2-06522947a8d8n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107769&group=sci.math#107769

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1a10:b0:31f:16be:c2bc with SMTP id f16-20020a05622a1a1000b0031f16bec2bcmr10563906qtb.175.1659269167857;
Sun, 31 Jul 2022 05:06:07 -0700 (PDT)
X-Received: by 2002:a9d:4f0a:0:b0:61c:ae80:3d36 with SMTP id
d10-20020a9d4f0a000000b0061cae803d36mr4451927otl.151.1659269167621; Sun, 31
Jul 2022 05:06:07 -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: Sun, 31 Jul 2022 05:06:07 -0700 (PDT)
In-Reply-To: <e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:563f:50ae:104f:a186:1f2a;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:563f:50ae:104f:a186:1f2a
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>
<e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d86f0df8-3f98-48a5-88b2-06522947a8d8n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 31 Jul 2022 12:06:07 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 4788

by: WM - Sun, 31 Jul 2022 12:06 UTC

Re: Natural numbers and vases III

<f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107770&group=sci.math#107770

copy link Newsgroups: sci.math

X-Received: by 2002:a37:648f:0:b0:6b5:ccd2:3ff9 with SMTP id y137-20020a37648f000000b006b5ccd23ff9mr8474873qkb.139.1659269317867;
Sun, 31 Jul 2022 05:08:37 -0700 (PDT)
X-Received: by 2002:a05:6808:1983:b0:33a:a390:8457 with SMTP id
bj3-20020a056808198300b0033aa3908457mr4432811oib.169.1659269317666; Sun, 31
Jul 2022 05:08:37 -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: Sun, 31 Jul 2022 05:08:37 -0700 (PDT)
In-Reply-To: <78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:563f:50ae:104f:a186:1f2a;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:563f:50ae:104f:a186:1f2a
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>
<78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 31 Jul 2022 12:08:37 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 4721

by: WM - Sun, 31 Jul 2022 12:08 UTC

Re: Natural numbers and vases III

<e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107771&group=sci.math#107771

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:2844:b0:6b8:5f52:a6b5 with SMTP id h4-20020a05620a284400b006b85f52a6b5mr8491912qkp.351.1659269863905;
Sun, 31 Jul 2022 05:17:43 -0700 (PDT)
X-Received: by 2002:a05:6808:18a6:b0:33b:1efb:56de with SMTP id
bi38-20020a05680818a600b0033b1efb56demr4707740oib.221.1659269863640; Sun, 31
Jul 2022 05:17:43 -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: Sun, 31 Jul 2022 05:17:43 -0700 (PDT)
In-Reply-To: <961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:563f:50ae:104f:a186:1f2a;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:563f:50ae:104f:a186:1f2a
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com> <e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net> <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 31 Jul 2022 12:17:43 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3690

by: WM - Sun, 31 Jul 2022 12:17 UTC

Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
> On 7/30/2022 8:31 AM, WM wrote:
> > Jim Burns schrieb
> > am Freitag, 29. Juli 2022 um 18:55:08 UTC+2:
>
> >> WM-dark numbers, end segments, fractions
> >> can be hypothetically added to a WM-incomplete
> >> subset to produce a WM-complete set.
> >
> > Very good!
> >
> >> the dark remainder can match itself,
> >
> > No.
> Typically, claims in the definition are
> easy to grant acceptance.

Dark means not discernible.
>
> Here, your Alfred and my Betty have no common
> ground to dispute. Your things which cannot match
> themselves are not things which we are talking
> about.

But you claim that all natural numbers are definable which is not a matter of taste but blatantly wrong.

Take the intersection of all endsegments which together have an infinite intersection. You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection.

> >> WM-completeness requires elements which
> >> _cannot_ match themselves.
> >
> > Yes.
> Consider the Pythagorean theorem.
> There is a triangle ABC such that
> |AB|² ≠ |AC|² + |BC|²
>
> ABC is not a right triangle.
> Does it disprove the theorem?

No, but it would disprove your claim, if you claimed that all triangles are rectangular --- like you claim that all numbers are definable.

Regards, WM

Re: Natural numbers and vases III

<78eb608f-e3ba-4933-bd5f-e1d2d566bfean@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107772&group=sci.math#107772

copy link Newsgroups: sci.math

X-Received: by 2002:a37:a54:0:b0:6b5:ccf3:a0ad with SMTP id 81-20020a370a54000000b006b5ccf3a0admr8704145qkk.612.1659275058701;
Sun, 31 Jul 2022 06:44:18 -0700 (PDT)
X-Received: by 2002:a05:6830:6183:b0:616:a125:1f84 with SMTP id
cb3-20020a056830618300b00616a1251f84mr4427003otb.350.1659275058455; Sun, 31
Jul 2022 06:44:18 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.misty.com!border-2.nntp.ord.giganews.com!nntp.giganews.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sun, 31 Jul 2022 06:44:18 -0700 (PDT)
In-Reply-To: <f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.125.241; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.125.241
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>
<78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com> <f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <78eb608f-e3ba-4933-bd5f-e1d2d566bfean@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sun, 31 Jul 2022 13:44:18 +0000
Content-Type: text/plain; charset="UTF-8"
Lines: 4

by: Gus Gassmann - Sun, 31 Jul 2022 13:44 UTC

Re: Natural numbers and vases III

<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107776&group=sci.math#107776

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:c68a:0:b0:46b:8e6b:306 with SMTP id d10-20020a0cc68a000000b0046b8e6b0306mr10625894qvj.7.1659279810263;
Sun, 31 Jul 2022 08:03:30 -0700 (PDT)
X-Received: by 2002:a05:6830:11c6:b0:61c:c75b:7fa5 with SMTP id
v6-20020a05683011c600b0061cc75b7fa5mr4566877otq.243.1659279809987; Sun, 31
Jul 2022 08:03:29 -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: Sun, 31 Jul 2022 08:03:29 -0700 (PDT)
In-Reply-To: <664cb6fe-940a-4df1-b9c8-f538e3682464n@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>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Sun, 31 Jul 2022 15:03:30 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5204

by: William - Sun, 31 Jul 2022 15:03 UTC

Re: Natural numbers and vases III

<tc665s$1eq9$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107777&group=sci.math#107777

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: Sun, 31 Jul 2022 10:12:59 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tc665s$1eq9$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com>
<e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net>
<bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
<e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="47945"; 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/91.11.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Sun, 31 Jul 2022 15:12 UTC

On 7/31/2022 7:17 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
>> On 7/30/2022 8:31 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Freitag, 29. Juli 2022 um 18:55:08 UTC+2:
>>
>>>> WM-dark numbers, end segments, fractions
>>>> can be hypothetically added to a WM-incomplete
>>>> subset to produce a WM-complete set.
>>>
>>> Very good!
>>>
>>>> the dark remainder can match itself,
>>>
>>> No.
>> Typically, claims in the definition are
>> easy to grant acceptance.
>
> Dark means not discernible.

Which means Dark numbers do not exist.

>>
>> Here, your Alfred and my Betty have no common
>> ground to dispute. Your things which cannot match
>> themselves are not things which we are talking
>> about.
>
> But you claim that all natural numbers are definable which is not a matter of taste but blatantly wrong.

Wrong, every natural number is a member of a FISON.

>
> Take the intersection of all endsegments which together have an infinite intersection.

More Wrong. It is empty, and not an endsegment.

> You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection.

Misleading Garf.

>
>>>> WM-completeness requires elements which
>>>> _cannot_ match themselves.
>>>
>>> Yes.
>> Consider the Pythagorean theorem.
>> There is a triangle ABC such that
>> |AB|² ≠ |AC|² + |BC|²
>>
>> ABC is not a right triangle.
>> Does it disprove the theorem?
>
> No, but it would disprove your claim, if you claimed that all triangles are rectangular

Wrong, he did not claim that, you made it up.

> --- like you claim that all numbers are definable.

Wrong.

>
> Regards, WM
>
>

WM the Miss Leader, troll, and dispenser of Red Herrings and Bad Math, errors in every post.

Re: Natural numbers and vases III

<tc667h$1eq9$2@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107778&group=sci.math#107778

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: Sun, 31 Jul 2022 10:13:53 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tc667h$1eq9$2@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<91e4d6a2-a525-42c3-b019-d1bd2d1df896n@googlegroups.com>
<16e00901-5498-4c37-8065-15bd37e3c901n@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="47945"; 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/91.11.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Sun, 31 Jul 2022 15:13 UTC

Re: Natural numbers and vases III

<tc66a9$1eq9$3@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107779&group=sci.math#107779

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: Sun, 31 Jul 2022 10:15:21 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tc66a9$1eq9$3@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com>
<f38e6e91-eb09-46ce-9b05-7436e42c589cn@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="47945"; 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/91.11.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Sun, 31 Jul 2022 15:15 UTC

Re: Natural numbers and vases III

<tc66i5$1k9v$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107780&group=sci.math#107780

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: Sun, 31 Jul 2022 10:19:32 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tc66i5$1k9v$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com>
<d86f0df8-3f98-48a5-88b2-06522947a8d8n@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="53567"; 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/91.11.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Sergio - Sun, 31 Jul 2022 15:19 UTC

On 7/31/2022 7:06 AM, WM wrote:
> Fritz Feldhase schrieb am Samstag, 30. Juli 2022 um 19:23:40 UTC+2:
>> On Friday, July 29, 2022 at 4:00:09 PM UTC+2, WM wrote:
>>
>>> Induction is doubtful
>>
>> Another keeper! :-)
>
> Induction proves that not all natural numbers are subject to induction.

Another Keeper!!!

> Induction concerns definable natural numbers,

Wrong. Induction is used on all types of numbers.

>a vanishing minority compared to the dark natural numbers following upon every definable natural number,

Wrong, your vision of your darkies is Kaput, Your "definable" is a QuAck Fest

< further garf snipped>

> Regards, WM

Re: Natural numbers and vases III

<4e2f85d3-988f-4839-b6b5-cd5ae813525bn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107784&group=sci.math#107784

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:1a8b:b0:31f:82e:8b1c with SMTP id s11-20020a05622a1a8b00b0031f082e8b1cmr11071438qtc.659.1659283701871;
Sun, 31 Jul 2022 09:08:21 -0700 (PDT)
X-Received: by 2002:a4a:a3cd:0:b0:435:c5f1:fabd with SMTP id
t13-20020a4aa3cd000000b00435c5f1fabdmr4224958ool.61.1659283701618; Sun, 31
Jul 2022 09:08:21 -0700 (PDT)
Path: i2pn2.org!i2pn.org!aioe.org!news.uzoreto.com!news-out.netnews.com!news.alt.net!fdc2.netnews.com!peer03.ams1!peer.ams1.xlned.com!news.xlned.com!peer03.ams4!peer.am4.highwinds-media.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: Sun, 31 Jul 2022 09:08:21 -0700 (PDT)
In-Reply-To: <f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.197.37; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.197.37
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>
<78492f9e-f6b1-4d5d-96c8-14943412ac82n@googlegroups.com> <f38e6e91-eb09-46ce-9b05-7436e42c589cn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <4e2f85d3-988f-4839-b6b5-cd5ae813525bn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sun, 31 Jul 2022 16:08:21 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 4742

by: Fritz Feldhase - Sun, 31 Jul 2022 16:08 UTC

Re: Natural numbers and vases III

<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107786&group=sci.math#107786

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:4017:b0:476:6229:bbf8 with SMTP id kd23-20020a056214401700b004766229bbf8mr4600876qvb.14.1659284088242;
Sun, 31 Jul 2022 09:14:48 -0700 (PDT)
X-Received: by 2002:a9d:58cc:0:b0:61c:efc0:5c75 with SMTP id
s12-20020a9d58cc000000b0061cefc05c75mr4708533oth.167.1659284088011; Sun, 31
Jul 2022 09:14:48 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sun, 31 Jul 2022 09:14:47 -0700 (PDT)
In-Reply-To: <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.197.37; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.197.37
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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> <abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com> <e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net> <bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net> <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sun, 31 Jul 2022 16:14:48 +0000
Content-Type: text/plain; charset="UTF-8"

by: Fritz Feldhase - Sun, 31 Jul 2022 16:14 UTC

On Sunday, July 31, 2022 at 2:17:48 PM UTC+2, WM wrote:
> Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
>
> Take the intersection of all endsegments which together have an infinite intersection.

I'd like to take the set "of all endsegments which together have an infinite intersection" first.

Can you define that set using the usual symbolic language of set theory?

Say,

WM := {E e Set_of_Endsegments : <a predicate concerning E, stated in the usual symbolic language of set theory>} .

Can you do this?

Alternatively, you may state this definition the following way to:

E e WM <-> E e Set_of_Endsegments & <a predicate concerning E, stated in the usual symbolic language of set theory> .

Re: Natural numbers and vases III

<9bfc4df7-a3ce-cca2-6383-c87066ca9207@att.net>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107799&group=sci.math#107799

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 31 Jul 2022 16:10:00 -0400
Organization: A noiseless patient Spider
Lines: 109
Message-ID: <9bfc4df7-a3ce-cca2-6383-c87066ca9207@att.net>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com>
<e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net>
<bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
<e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: reader01.eternal-september.org; posting-host="bc577a42acbf85a162b82910520dbc54";
logging-data="516841"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+ZqnC8thxvw9IAiCPCiqYx0+qozxJBu+Q="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.11.0
Cancel-Lock: sha1:Hh9kE2Ia+nk0qMnJmfqUMQEABdA=
In-Reply-To: <e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
Content-Language: en-US

by: Jim Burns - Sun, 31 Jul 2022 20:10 UTC

On 7/31/2022 8:17 AM, WM wrote:
> Jim Burns schrieb
> am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
>> On 7/30/2022 8:31 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Freitag, 29. Juli 2022 um 18:55:08 UTC+2:

>>>> WM-dark numbers, end segments, fractions
>>>> can be hypothetically added to a WM-incomplete
>>>> subset to produce a WM-complete set.
>>>
>>> Very good!
>>>
>>>> the dark remainder can match itself,
>>>
>>> No.
>>
>> Typically, claims in the definition are
>> easy to grant acceptance.
>
> Dark means not discernible.

Dark means that they can WM-complete
a WM-incomplete collection.

Things which can WM-complete a WM-incomplete set
are not things the rest of us are talking about.

>> Here, your Alfred and my Betty have no common
>> ground to dispute. Your things which cannot match
>> themselves are not things which we are talking
>> about.
>
> But you claim that all natural numbers are
> definable

I claim that natural numbers are things in FISONs.
It's a definition.

_Everything_ I'm talking about is equal to itself.
Apparently, you and I have no common ground
to dispute.

> which is not a matter of taste
> but blatantly wrong.

If Alfred and Betty define naturals differently,
the one's conclusions may not apply to the other's,
and the other's may not apply to the one's.
There might not be common ground to dispute.

> Take the intersection of all endsegments which
> together have an infinite intersection.

For end segments of things in FISONs,
either
some thing is in their intersection
xor
some end segment is not-in their collection.

The intersection of _all_ end segments
has nothing in it.

> You cannot define other endsegments.
> But you claim that there are more,
> namely enough to yield an empty intersection.

_These_ end segments by themselves
have an empty intersection.
It is _all_ of _these_ end segments
which have an empty intersection.

>>>> WM-completeness requires elements which
>>>> _cannot_ match themselves.
>>>
>>> Yes.
>>
>> Consider the Pythagorean theorem.
>> There is a triangle ABC such that
>> |AB|² ≠ |AC|² + |BC|²
>>
>> ABC is not a right triangle.
>> Does it disprove the theorem?
>
> No,

No, _because_
the Pythagorean theorem is talking about
_right triangles_ not merely triangles.

WM-completeness requires elements which
_cannot_ match themselves. Dark elements.

Nothing which we are talking about
cannot match itself.
WM-completeness _does not happen_ with
what we're talking about.

If Alfred and Betty define naturals differently,
the one's conclusions may not apply to the other's,
and the other's may not apply to the one's.
There might not be common ground to dispute.

> but it would disprove your claim,
> if you claimed that all triangles are rectangular
> --- like you claim that all numbers are definable.

Re: Natural numbers and vases III

<e8ab7d54-9f60-6599-d196-016d165039e8@att.net>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107801&group=sci.math#107801

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 31 Jul 2022 17:24:14 -0400
Organization: A noiseless patient Spider
Lines: 33
Message-ID: <e8ab7d54-9f60-6599-d196-016d165039e8@att.net>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<abd642e5-f08f-46ab-be80-15278d1d1fa3n@googlegroups.com>
<a211e827-701c-45d4-bcae-594875b7d27bn@googlegroups.com>
<e37f14f5-2810-41b5-92d6-18ba6c4481b1n@googlegroups.com>
<fa4b3578-4766-c438-7a94-1dd2bdbcd643@att.net>
<bd26ea53-764c-4fa8-afdb-5ca01d2d6b50n@googlegroups.com>
<961dd9ff-22e3-6739-ce41-0ef4968bd32f@att.net>
<e847cfdd-9c53-4f85-823b-60d3b0abf7e9n@googlegroups.com>
<9bfc4df7-a3ce-cca2-6383-c87066ca9207@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: reader01.eternal-september.org; posting-host="bc577a42acbf85a162b82910520dbc54";
logging-data="529308"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18ZDo2XysD/iERc2+2YvrPjNrUxQtAroI0="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.11.0
Cancel-Lock: sha1:z65VEL+GLt1xzmj+jR1I1SlSSpA=
Content-Language: en-US
In-Reply-To: <9bfc4df7-a3ce-cca2-6383-c87066ca9207@att.net>

by: Jim Burns - Sun, 31 Jul 2022 21:24 UTC

On 7/31/2022 4:10 PM, Jim Burns wrote:
> On 7/31/2022 8:17 AM, WM wrote:

>> Take the intersection of all endsegments which
>> together have an infinite intersection.
>
> For end segments of things in FISONs,
> either
> some thing is in their intersection
> xor
> some end segment is not-in their collection.

Whoops. Not what I intended to say.

For things in FISONs,
for end segments of those things,
for collections of end segments of those things,
If
its intersection has a thing in it,
then
the collection has an end segment not in it.

If
the collection has all end segments in it,
then
its intersection doesn't have a thing in it.

> The intersection of _all_ end segments
> has nothing in it.

This, I meant to say.

Re: Natural numbers and vases III

<31ff33ac-5809-4eaf-8197-2407a7258bd0n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=107823&group=sci.math#107823

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:c2a:b0:473:7a9a:17ae with SMTP id a10-20020a0562140c2a00b004737a9a17aemr12442126qvd.57.1659331530137;
Sun, 31 Jul 2022 22:25:30 -0700 (PDT)
X-Received: by 2002:aca:1103:0:b0:33a:c295:f483 with SMTP id
3-20020aca1103000000b0033ac295f483mr6290885oir.80.1659331529870; Sun, 31 Jul
2022 22:25:29 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sun, 31 Jul 2022 22:25:29 -0700 (PDT)
In-Reply-To: <d86f0df8-3f98-48a5-88b2-06522947a8d8n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=45.83.91.190; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 45.83.91.190
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>
<e6e38213-f5d3-405f-b128-0fb2a5739434n@googlegroups.com> <d86f0df8-3f98-48a5-88b2-06522947a8d8n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <31ff33ac-5809-4eaf-8197-2407a7258bd0n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Mon, 01 Aug 2022 05:25:30 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 4945

by: zelos...@gmail.com - Mon, 1 Aug 2022 05:25 UTC

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