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

Re: Natural numbers and vases III

<4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>

https://www.novabbs.com/tech/article-flat.php?id=108004&group=sci.math#108004

X-Received: by 2002:a05:620a:470e:b0:6b5:ed19:5a with SMTP id bs14-20020a05620a470e00b006b5ed19005amr16363796qkb.55.1659475033274;
Tue, 02 Aug 2022 14:17:13 -0700 (PDT)
X-Received: by 2002:a05:6808:198a:b0:33f:46b4:9f0b with SMTP id
bj10-20020a056808198a00b0033f46b49f0bmr541986oib.242.1659475032802; Tue, 02
Aug 2022 14:17:12 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 2 Aug 2022 14:17:12 -0700 (PDT)
In-Reply-To: <39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:4928:540c:d978:d07d:7f6b;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:4928:540c:d978:d07d:7f6b
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 02 Aug 2022 21:17:13 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 5339

by: WM - Tue, 2 Aug 2022 21:17 UTC

Re: Natural numbers and vases III

<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108005&group=sci.math#108005

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5761:0:b0:473:7861:69d1 with SMTP id r1-20020ad45761000000b00473786169d1mr20034787qvx.73.1659475726112;
Tue, 02 Aug 2022 14:28:46 -0700 (PDT)
X-Received: by 2002:a05:6808:13d2:b0:33a:7651:3ab3 with SMTP id
d18-20020a05680813d200b0033a76513ab3mr534700oiw.277.1659475725864; Tue, 02
Aug 2022 14:28:45 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 2 Aug 2022 14:28:45 -0700 (PDT)
In-Reply-To: <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Tue, 02 Aug 2022 21:28:46 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5266

by: William - Tue, 2 Aug 2022 21:28 UTC

Re: Natural numbers and vases III

<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108016&group=sci.math#108016

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:5703:0:b0:31e:f79b:9ecc with SMTP id 3-20020ac85703000000b0031ef79b9eccmr20327050qtw.192.1659502322818;
Tue, 02 Aug 2022 21:52:02 -0700 (PDT)
X-Received: by 2002:a05:6870:b68f:b0:10b:ba83:92d4 with SMTP id
cy15-20020a056870b68f00b0010bba8392d4mr1122933oab.130.1659502321452; Tue, 02
Aug 2022 21:52:01 -0700 (PDT)
Path: i2pn2.org!rocksolid2!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 2 Aug 2022 21:52:01 -0700 (PDT)
In-Reply-To: <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=185.219.140.251; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 185.219.140.251
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>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Wed, 03 Aug 2022 04:52:02 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3267

by: zelos...@gmail.com - Wed, 3 Aug 2022 04:52 UTC

Re: Natural numbers and vases III

<1b032683-3775-4cdb-a2f6-821a88670833n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108034&group=sci.math#108034

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:561:b0:6b6:1b3a:5379 with SMTP id p1-20020a05620a056100b006b61b3a5379mr18085821qkp.111.1659522346487;
Wed, 03 Aug 2022 03:25:46 -0700 (PDT)
X-Received: by 2002:a05:6808:198a:b0:33f:46b4:9f0b with SMTP id
bj10-20020a056808198a00b0033f46b49f0bmr1378543oib.242.1659522346218; Wed, 03
Aug 2022 03:25:46 -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: Wed, 3 Aug 2022 03:25:45 -0700 (PDT)
In-Reply-To: <bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:c0b0:7f24:427b:8e4e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:c0b0:7f24:427b:8e4e
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1b032683-3775-4cdb-a2f6-821a88670833n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 10:25:46 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5484

by: WM - Wed, 3 Aug 2022 10:25 UTC

Re: Natural numbers and vases III

<d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108036&group=sci.math#108036

copy link Newsgroups: sci.math

X-Received: by 2002:ac8:7d90:0:b0:326:b431:6cd3 with SMTP id c16-20020ac87d90000000b00326b4316cd3mr15603484qtd.511.1659524419150;
Wed, 03 Aug 2022 04:00:19 -0700 (PDT)
X-Received: by 2002:a05:6870:1607:b0:101:a7a7:3ece with SMTP id
b7-20020a056870160700b00101a7a73ecemr1588803oae.99.1659524418931; Wed, 03 Aug
2022 04:00:18 -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: Wed, 3 Aug 2022 04:00:18 -0700 (PDT)
In-Reply-To: <bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:c0b0:7f24:427b:8e4e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:c0b0:7f24:427b:8e4e
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 11:00:19 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5912

by: WM - Wed, 3 Aug 2022 11:00 UTC

Re: Natural numbers and vases III

<5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108037&group=sci.math#108037

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:204:b0:31f:3bb:3294 with SMTP id b4-20020a05622a020400b0031f03bb3294mr21186762qtx.436.1659524436483;
Wed, 03 Aug 2022 04:00:36 -0700 (PDT)
X-Received: by 2002:a05:6808:169e:b0:331:522a:4521 with SMTP id
bb30-20020a056808169e00b00331522a4521mr1457156oib.293.1659524436290; Wed, 03
Aug 2022 04:00:36 -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: Wed, 3 Aug 2022 04:00:36 -0700 (PDT)
In-Reply-To: <672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:c0b0:7f24:427b:8e4e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:c0b0:7f24:427b:8e4e
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>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 11:00:36 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3883

by: WM - Wed, 3 Aug 2022 11:00 UTC

zelos...@gmail.com schrieb am Mittwoch, 3. August 2022 um 06:52:07 UTC+2:
> tisdag 2 augusti 2022 kl. 17:31:40 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> > > måndag 1 augusti 2022 kl. 13:28:50 UTC+2 skrev WM:
> >
> > > > > Can you define that set using the usual symbolic language of set theory?
> > > > The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}
> > > >
> > > your N_def = N so you have said nothing
> > If you claim that the intersection of all definable endsegments is empty, then define individually endsegments reducing the infinite intersection to the empty set.
> >
> your "define individually" is meaningless. the intersection is empty because n is not in E(n+1)
>
> Simple as that. there is nothing else to it

There is but a minor detail: All definable endsegments appearing in
∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
can be subtracted from {E(k) : k ∈ ℕ} without changing the result.

∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }

This proves the existence of dark numbers.

Regards, WM

Re: Natural numbers and vases III

<5b76f555-35b9-4a6f-a8dd-26a2a3cb0b34n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108038&group=sci.math#108038

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:4eec:0:b0:476:b2b2:1809 with SMTP id dv12-20020ad44eec000000b00476b2b21809mr9428491qvb.40.1659525227115;
Wed, 03 Aug 2022 04:13:47 -0700 (PDT)
X-Received: by 2002:a05:6830:2709:b0:61c:c396:94f2 with SMTP id
j9-20020a056830270900b0061cc39694f2mr9564312otu.369.1659525226811; Wed, 03
Aug 2022 04:13:46 -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: Wed, 3 Aug 2022 04:13:46 -0700 (PDT)
In-Reply-To: <f5118003-1296-48e5-8aa7-cf6ae103f1b1n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:c0b0:7f24:427b:8e4e;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:c0b0:7f24:427b:8e4e
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>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com> <c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com> <aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<ef12bf23-e642-48cb-aee6-fb6726adcfccn@googlegroups.com> <d27a3cba-0526-4cb1-a498-37e28f8be59cn@googlegroups.com>
<f5118003-1296-48e5-8aa7-cf6ae103f1b1n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <5b76f555-35b9-4a6f-a8dd-26a2a3cb0b34n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 11:13:47 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 3960

by: WM - Wed, 3 Aug 2022 11:13 UTC

Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 23:15:26 UTC+2:
> On Tuesday, August 2, 2022 at 10:36:29 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 18:10:39 UTC+2:
> > > On Tuesday, August 2, 2022 at 5:31:40 PM UTC+2, WM wrote:
> > > > zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> > > > >
> > > > > Your N_def = N so you have said nothing.
> > > > >
> > > > If you claim that the intersection of all [...] endsegments is empty, then define [specific] endsegments reducing the infinite intersection to the empty set.
> > >
> > > There are no such endsegments,
> > >
> > There are.
> No, there aren't. Hint: INTERSECTION {E(1), E(3), E(5), ...} = INTERSECTION {E(2), E(4), E(6), ...} = { }.

All definable endsegments appearing in
∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
can be subtracted from {E(k) : k ∈ ℕ} without changing the result.

∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }

This proves that there are special endsegment responsible for the empty intersection, but they are dark and therefore you cannot see them.

Regards, WM

Re: Natural numbers and vases III

<tcdps9$1q7v$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108039&group=sci.math#108039

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: Wed, 3 Aug 2022 07:32:08 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcdps9$1q7v$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com>
<c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com>
<aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<ef12bf23-e642-48cb-aee6-fb6726adcfccn@googlegroups.com>
<d27a3cba-0526-4cb1-a498-37e28f8be59cn@googlegroups.com>
<f5118003-1296-48e5-8aa7-cf6ae103f1b1n@googlegroups.com>
<5b76f555-35b9-4a6f-a8dd-26a2a3cb0b34n@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="59647"; 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 - Wed, 3 Aug 2022 12:32 UTC

On 8/3/2022 6:13 AM, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 23:15:26 UTC+2:
>> On Tuesday, August 2, 2022 at 10:36:29 PM UTC+2, WM wrote:
>>> Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 18:10:39 UTC+2:
>>>> On Tuesday, August 2, 2022 at 5:31:40 PM UTC+2, WM wrote:
>>>>> zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
>>>>>>
>>>>>> Your N_def = N so you have said nothing.
>>>>>>
>>>>> If you claim that the intersection of all [...] endsegments is empty, then define [specific] endsegments reducing the infinite intersection to the empty set.
>>>>
>>>> There are no such endsegments,
>>>>
>>> There are.
>> No, there aren't. Hint: INTERSECTION {E(1), E(3), E(5), ...} = INTERSECTION {E(2), E(4), E(6), ...} = { }.
>
> All definable endsegments appearing in
> ∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
> can be subtracted from {E(k) : k ∈ ℕ} without changing the result.
>
> ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }
>
> This proves

QUAcK!! you proved nothing except your incompetence.

> that there are special endsegment responsible for the empty intersection, but they are dark and therefore you cannot see them.

then get your flashlight,

you have retreated into your imagination, and there are darkies there but you cannot see them.

>
> Regards, WM
>

Re: Natural numbers and vases III

<tcdpvs$1q7v$2@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108040&group=sci.math#108040

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: Wed, 3 Aug 2022 07:34:04 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcdpvs$1q7v$2@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@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>
<46466756-d94a-43d9-a92a-31865c08fbc0n@googlegroups.com>
<c8541e86-b7a1-4f69-82e5-08a1eed63acen@googlegroups.com>
<c293ac33-eec1-4456-bcd0-0396e5805d9dn@googlegroups.com>
<aa78bf0b-0115-4b27-9cbe-932f86408d46n@googlegroups.com>
<672461ec-2b45-4e5c-aab5-bfa7cb46bc42n@googlegroups.com>
<5cab820f-ad90-48e6-adc2-455e944225b9n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="59647"; 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 - Wed, 3 Aug 2022 12:34 UTC

On 8/3/2022 6:00 AM, WM wrote:
> zelos...@gmail.com schrieb am Mittwoch, 3. August 2022 um 06:52:07 UTC+2:
>> tisdag 2 augusti 2022 kl. 17:31:40 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
>>>> måndag 1 augusti 2022 kl. 13:28:50 UTC+2 skrev WM:
>>>
>>>>>> Can you define that set using the usual symbolic language of set theory?
>>>>> The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}
>>>>>
>>>> your N_def = N so you have said nothing
>>> If you claim that the intersection of all definable endsegments is empty, then define individually endsegments reducing the infinite intersection to the empty set.
>>>
>> your "define individually" is meaningless. the intersection is empty because n is not in E(n+1)
>>
>> Simple as that. there is nothing else to it
>

QuacK!!

no math at all

>
> Regards, WM

your "define individually" is meaningless. the intersection is empty because n is not in E(n+1)

Re: Natural numbers and vases III

<tcdq53$1q7v$3@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108041&group=sci.math#108041

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: Wed, 3 Aug 2022 07:36:51 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcdq53$1q7v$3@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com>
<eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com>
<d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
<664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>
<8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com>
<edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com>
<55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
<4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
<d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="59647"; 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 - Wed, 3 Aug 2022 12:36 UTC

Re: Natural numbers and vases III

<tcdrof$ofj$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108043&group=sci.math#108043

copy link Newsgroups: sci.math
Followup: sci.physics.relativity

Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!news.mixmin.net!aioe.org!3trAmE1COidd01QrdQuawQ.user.46.165.242.75.POSTED!not-for-mail
From: ono...@dooouobb.mo (Duan Bonomo)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Followup-To: sci.physics.relativity
Date: Wed, 3 Aug 2022 13:04:16 -0000 (UTC)
Organization: Aioe.org NNTP Server
Message-ID: <tcdrof$ofj$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com>
<d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
<664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>
<8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com>
<edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com>
<55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
<4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
<d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<tcdq53$1q7v$3@gioia.aioe.org>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="25075"; posting-host="3trAmE1COidd01QrdQuawQ.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:60.0) Gecko/20100101
Firefox/60.0 SeaMonkey/2.53.7.1
X-Notice: Filtered by postfilter v. 0.9.2
X-Face: "d\S.?wFfRfWKkKlnvU%l.LN_$_!,8scLw4d\sThzx"s.Iy^.y7f<oEXw;r/Bk!'
5BP'+HO3(,(FZq|]u(`4svg1~RN[sz|8nOT=%abJ@q_DR;G4l\{6c(.&*u:KvA%?/~Ia_2-
h[-=R9JgGApp+%i{,S/P[lsDBjAw|@ibdm^p1ncb6qN`C?]1Z6Auu7b}n-339r.s697]=R9
[r>q^pv%,r:M]VJQFzkdkf#[5St#Aw@:v'=vdev?4&Qx6,LW77'l!#FiJ"9H??"5X#$l!/(
$RuaFr!.frxe~=)].vgYLx$0ML!5^F;&gggZo7n(*?2bkJ@vG[Ga&@+qA9Zh7,Z_al@pZ.
Face: iVBORw0KGgoAAAANSUhEUgAAADAAAAAwBAMAAAClLOS0AAAAGFBMVEVbPSRthZjI
tpLs1s+7gXcZGx66xs5kXFOmyn6MAAACfUlEQVQ4jXWTPW/jMAyGmcI6ze7grgU
t1LsdpKur40GrC5TwnBZwV6VQo79/r5ykDe5D8GDzMT9ekqLhP4eWf526bqjZve
3wult23/Z9XdfULGdwZb4Cb7s/Qv0N6pzrEusMHvZn+51R1cO+OYPX2/3TbbG/U
87ZaL3Up6qc30puAGK+yznqXJ/AK7fbbEH2MxysNXo862jbbaxos7znGHPMn/q8
ACzDrm8fSSZq7gkJdCJVeCzLMPTcJae0uXM+RNVZ9ViqGgYWwn80H3p2kiNdwCv
/mmxCNRXDWSQY/QEAB6aKmcXMvi1fLp7B4KwH4HE6AZYS6m3Y8X1qEYPDJCfgzJ
GKA1P5E6V9g4ZQ065D0sLdF9AC+s4gUvFw5+QrGIZOp1MkkSn5FXTzAjACrF9WK
JNn13KHXg19NDP3LrUdGp6zf6TkXQGOzAsqzW0XZEzi71NOsqlpCaQv7IK0Tnwn
ws6nJLmmHimqoRVe03gGR7MOC/VRqVqXEtJH77g0J3zsaUuzLbIuoHeQMTYLbY1
94Z8r8DyKHwCwGHvqMB+GrH7bCX+K4wCwWRbqMC/mduBeWGLC4104AriQzQ0AEC
ZlI32whGZpCBKM3rT94Ea0hGysBCqwcH1ZhJvSE/FuqlKkFJACLWGONENYD6AJ4
lJ8vgBrKm6hLGg1IhJNhxLK+ZziJHDhqC9oSJ7VroAlhbI4GLnOUK8b7CQAJiNS
dk0+cWc+HGlSBKMtQmcJWGUtZzITpakA6BWbgl7ONOWsajMEPmWM7GwlrHYOK+j
o5jXI4QKK9giviMs4PSDLVyi1pMYWgKso10BNSZMLQCPGK6BkV2AMXCDBfAPY82
9KvR63cX6edQAAAABJRU5ErkJggg==

by: Duan Bonomo - Wed, 3 Aug 2022 13:04 UTC

Re: Natural numbers and vases III

<06a60654-712c-49db-b575-933f2c76fc21n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108044&group=sci.math#108044

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:258c:b0:476:6879:eade with SMTP id fq12-20020a056214258c00b004766879eademr14869660qvb.69.1659533631013;
Wed, 03 Aug 2022 06:33:51 -0700 (PDT)
X-Received: by 2002:a05:6808:1983:b0:33a:a390:8457 with SMTP id
bj3-20020a056808198300b0033aa3908457mr1570269oib.169.1659533630751; Wed, 03
Aug 2022 06:33:50 -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: Wed, 3 Aug 2022 06:33:50 -0700 (PDT)
In-Reply-To: <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <06a60654-712c-49db-b575-933f2c76fc21n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Wed, 03 Aug 2022 13:33:51 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5521

by: William - Wed, 3 Aug 2022 13:33 UTC

Re: Natural numbers and vases III

<8ac0722e-4346-4073-a81b-67a4096777fbn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108045&group=sci.math#108045

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:2909:b0:6b6:a94:a988 with SMTP id m9-20020a05620a290900b006b60a94a988mr18925789qkp.350.1659534411259;
Wed, 03 Aug 2022 06:46:51 -0700 (PDT)
X-Received: by 2002:a05:6808:1b8d:b0:32f:7995:b32b with SMTP id
cj13-20020a0568081b8d00b0032f7995b32bmr1690270oib.219.1659534410948; Wed, 03
Aug 2022 06:46:50 -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: Wed, 3 Aug 2022 06:46:50 -0700 (PDT)
In-Reply-To: <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:9885:7f04:2841:81ee;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:9885:7f04:2841:81ee
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <8ac0722e-4346-4073-a81b-67a4096777fbn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 13:46:51 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6098

by: WM - Wed, 3 Aug 2022 13:46 UTC

Re: Natural numbers and vases III

<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108046&group=sci.math#108046

copy link Newsgroups: sci.math

X-Received: by 2002:ad4:5c4b:0:b0:474:7aa4:b0ba with SMTP id a11-20020ad45c4b000000b004747aa4b0bamr22453267qva.49.1659535253095; Wed, 03 Aug 2022 07:00:53 -0700 (PDT)
X-Received: by 2002:a9d:62d2:0:b0:636:94a9:2e23 with SMTP id z18-20020a9d62d2000000b0063694a92e23mr56561otk.167.1659535252787; Wed, 03 Aug 2022 07:00:52 -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!feeder.usenetexpress.com!tr3.iad1.usenetexpress.com!69.80.99.11.MISMATCH!border-1.nntp.ord.giganews.com!nntp.giganews.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 3 Aug 2022 07:00:52 -0700 (PDT)
In-Reply-To: <d2beedd3-bec2-4785-a474-67967e335a64n@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@googlegr
oups.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@googlegrou
ps.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com> <ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com> <bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com> <af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com> <cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com> <6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com> <55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com> <2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com> <b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com> <ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com> <bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups
.com> <39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com> <bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Wed, 03 Aug 2022 14:00:53 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 29
X-Received-Bytes: 6249

by: William - Wed, 3 Aug 2022 14:00 UTC

On Wednesday, August 3, 2022 at 8:00:24 AM UTC-3, WM wrote:
> William schrieb am Dienstag, 2. August 2022 um 23:28:51 UTC+2:
> > On Tuesday, August 2, 2022 at 6:17:17 PM UTC-3, WM wrote:
> >
> > > > WM: The intersection of the "defined" (i.e. the first element has the property that it can be written down) endsegments is an infinite set.
> > > >
> > > > This is a triviality.
> > > It is!
> > And thus of no interest whatsoever. The important fact is
> >
> > WM: ∩{E(k) : k ∈ ℕ} ={}

> ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }

or more simply

∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }

This is trivial as ℕ_def is finite. It shows that there are endsections which have a first element with the property that it cannot be written down (note that it does have many other properties including the property that is is connected to 1 by a finite number of successor operations, it is not "dark"). It does not show that there are "dark numbers".

>
> This proves the existence of dark numbers.
>
> Regards, WM

Re: Natural numbers and vases III

<29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108047&group=sci.math#108047

copy link Newsgroups: sci.math

X-Received: by 2002:a0c:8bd2:0:b0:474:7d1a:eb5b with SMTP id a18-20020a0c8bd2000000b004747d1aeb5bmr22067074qvc.18.1659536072700;
Wed, 03 Aug 2022 07:14:32 -0700 (PDT)
X-Received: by 2002:a9d:7cc4:0:b0:61c:acaa:1c67 with SMTP id
r4-20020a9d7cc4000000b0061cacaa1c67mr9476101otn.311.1659536072459; Wed, 03
Aug 2022 07:14:32 -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: Wed, 3 Aug 2022 07:14:32 -0700 (PDT)
In-Reply-To: <537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:9885:7f04:2841:81ee;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:9885:7f04:2841:81ee
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 14:14:32 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6706

by: WM - Wed, 3 Aug 2022 14:14 UTC

William schrieb am Mittwoch, 3. August 2022 um 16:00:59 UTC+2:
> On Wednesday, August 3, 2022 at 8:00:24 AM UTC-3, WM wrote:
> > William schrieb am Dienstag, 2. August 2022 um 23:28:51 UTC+2:
> > > On Tuesday, August 2, 2022 at 6:17:17 PM UTC-3, WM wrote:
> > >
> > > > > WM: The intersection of the "defined" (i.e. the first element has the property that it can be written down) endsegments is an infinite set.
> > > > >
> > > > > This is a triviality.
> > > > It is!
> > > And thus of no interest whatsoever. The important fact is
> > >
> > > WM: ∩{E(k) : k ∈ ℕ} ={}
> > ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }
> or more simply
>
> ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
>
> This is trivial as ℕ_def is finite.

ℕ_def is finite without a fixed last element however. Many call it potentially infinite, that is it can be expanded without limit.

> It shows that there are endsections which have a first element with the property that it cannot be written down

Thank you for this confession. But you will be persecuted by matheologians for this statement.

> (note that it does have many other properties including the property that is is connected to 1 by a finite number of successor operations, it is not "dark"). It does not show that there are "dark numbers".

Let us call them numbers which cannot be written down. They may have other properties of natural numbers. But we cannot know.

Regards, WM

Re: Natural numbers and vases III

<60e59a1a-4567-4cfb-8b27-ae48c9464e7fn@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108049&group=sci.math#108049

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:131:b0:476:73ea:406b with SMTP id w17-20020a056214013100b0047673ea406bmr14381681qvs.94.1659538420574;
Wed, 03 Aug 2022 07:53:40 -0700 (PDT)
X-Received: by 2002:a05:6808:238d:b0:33a:7c9b:a1c7 with SMTP id
bp13-20020a056808238d00b0033a7c9ba1c7mr1856809oib.7.1659538420380; Wed, 03
Aug 2022 07:53:40 -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: Wed, 3 Aug 2022 07:53:40 -0700 (PDT)
In-Reply-To: <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <60e59a1a-4567-4cfb-8b27-ae48c9464e7fn@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Wed, 03 Aug 2022 14:53:40 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 5862

by: Gus Gassmann - Wed, 3 Aug 2022 14:53 UTC

Re: Natural numbers and vases III

<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108051&group=sci.math#108051

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:5194:b0:474:9b86:35f4 with SMTP id kl20-20020a056214519400b004749b8635f4mr18975392qvb.35.1659540172156;
Wed, 03 Aug 2022 08:22:52 -0700 (PDT)
X-Received: by 2002:a05:6870:8890:b0:101:db34:3ed6 with SMTP id
m16-20020a056870889000b00101db343ed6mr2193120oam.151.1659540171913; Wed, 03
Aug 2022 08:22:51 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 3 Aug 2022 08:22:51 -0700 (PDT)
In-Reply-To: <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.190.171; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.190.171
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Wed, 03 Aug 2022 15:22:52 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7543

by: William - Wed, 3 Aug 2022 15:22 UTC

On Wednesday, August 3, 2022 at 11:14:37 AM UTC-3, WM wrote:
> William schrieb am Mittwoch, 3. August 2022 um 16:00:59 UTC+2:
> > On Wednesday, August 3, 2022 at 8:00:24 AM UTC-3, WM wrote:
> > > William schrieb am Dienstag, 2. August 2022 um 23:28:51 UTC+2:
> > > > On Tuesday, August 2, 2022 at 6:17:17 PM UTC-3, WM wrote:
> > > >
> > > > > > WM: The intersection of the "defined" (i.e. the first element has the property that it can be written down) endsegments is an infinite set..
> > > > > >
> > > > > > This is a triviality.
> > > > > It is!
> > > > And thus of no interest whatsoever. The important fact is
> > > >
> > > > WM: ∩{E(k) : k ∈ ℕ} ={}
> > > ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }
> > or more simply
> >
> > ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
> >
> > This is trivial as ℕ_def is finite.
> ℕ_def is finite

correct

> without a fixed last element however.

Piffle.

> Many call it potentially infinite, that is it can be expanded without limit.
Note that even if we accept the fact that ℕ_def changes, it changes into something finite so
∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
is "always" true (ℕ_def "always" has a last element).

>it can be expanded without limit.
> > It shows that there are endsections which have a first element with the property that it cannot be written down
> Thank you for this confession. But you will be persecuted by matheologians for this statement.
> > (note that it does have many other properties including the property that is is connected to 1 by a finite number of successor operations, it is not "dark"). It does not show that there are "dark numbers".
> Let us call them numbers which cannot be written down.

Nope, there are many properties of "dark numbers" that do not hold for numbers which cannot be written down. (E.g. a "dark number"
is not connected to 1 by a finite number of successor operations)...

> They may have other properties of natural numbers. But we cannot know.

Of course we can There are many ways, e.g. induction, to know that a number which does not have the property "can be written down", has other properties.

--
William Hughes

Re: Natural numbers and vases III

<tce45u$kmu$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108052&group=sci.math#108052

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: Wed, 3 Aug 2022 10:27:57 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tce45u$kmu$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com>
<d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
<664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>
<8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com>
<edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com>
<55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
<4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
<d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>
<29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="21214"; 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 - Wed, 3 Aug 2022 15:27 UTC

On 8/3/2022 9:14 AM, WM wrote:
> William schrieb am Mittwoch, 3. August 2022 um 16:00:59 UTC+2:
>> On Wednesday, August 3, 2022 at 8:00:24 AM UTC-3, WM wrote:
>>> William schrieb am Dienstag, 2. August 2022 um 23:28:51 UTC+2:
>>>> On Tuesday, August 2, 2022 at 6:17:17 PM UTC-3, WM wrote:
>>>>
>>>>>> WM: The intersection of the "defined" (i.e. the first element has the property that it can be written down) endsegments is an infinite set.
>>>>>>
>>>>>> This is a triviality.
>>>>> It is!
>>>> And thus of no interest whatsoever. The important fact is
>>>>
>>>> WM: ∩{E(k) : k ∈ ℕ} ={}
>>> ∩({E(k) : k ∈ ℕ} \ {E(k) : k ∈ ℕ_def}) = { }
>> or more simply
>>
>> ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
>>
>> This is trivial as ℕ_def is finite.
>
> ℕ_def is finite without a fixed last element however.

so now ℕ_def is undefined. ℕ defined is undefined.

> Many call it potentially infinite, that is it can be expanded without limit.

no, sets are fixed they do not change.

>
>> It shows that there are endsections which have a first element with the property that it cannot be written down
>
> Thank you for this confession. But you will be persecuted by matheologians for this statement.
>
>> (note that it does have many other properties including the property that is is connected to 1 by a finite number of successor operations, it is not "dark"). It does not show that there are "dark numbers".
>
> Let us call them numbers which cannot be written down. They may have other properties of natural numbers. But we cannot know.

Since you cannot know, how can you say they have other properties ?

>
> Regards, WM

you are just wading around in circles in your own 20 foot deep bullshit.

Re: Natural numbers and vases III

<84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108053&group=sci.math#108053

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:1981:b0:6b5:cccf:62e1 with SMTP id bm1-20020a05620a198100b006b5cccf62e1mr18038519qkb.376.1659540813985;
Wed, 03 Aug 2022 08:33:33 -0700 (PDT)
X-Received: by 2002:a05:6808:1b8d:b0:32f:7995:b32b with SMTP id
cj13-20020a0568081b8d00b0032f7995b32bmr1894791oib.219.1659540813715; Wed, 03
Aug 2022 08:33:33 -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: Wed, 3 Aug 2022 08:33:33 -0700 (PDT)
In-Reply-To: <2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:771f:49df:9885:7f04:2841:81ee;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:771f:49df:9885:7f04:2841:81ee
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Wed, 03 Aug 2022 15:33:33 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6663

by: WM - Wed, 3 Aug 2022 15:33 UTC

William schrieb am Mittwoch, 3. August 2022 um 17:22:57 UTC+2:
> On Wednesday, August 3, 2022 at 11:14:37 AM UTC-3, WM wrote:

> > > ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
> > >
> > > This is trivial as ℕ_def is finite.
> > ℕ_def is finite
> correct
> > without a fixed last element however.
> Piffle.

Then define the last element.

> > Many call it potentially infinite, that is it can be expanded without limit.
> Note that even if we accept the fact that ℕ_def changes, it changes into something finite so
> ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
> is "always" true (ℕ_def "always" has a last element).

Yes. That is the property of potential infinity. But if you think to know the last element, then it is no longer the last element.

> > Let us call them numbers which cannot be written down.
> Nope, there are many properties of "dark numbers" that do not hold for numbers which cannot be written down. (E.g. a "dark number"
> is not connected to 1 by a finite number of successor operations)...

You cannot know it for unwritable numbers.

> > They may have other properties of natural numbers. But we cannot know.
> Of course we can There are many ways, e.g. induction, to know that a number which does not have the property "can be written down", has other properties.

Many.

Regards, WM

Re: Natural numbers and vases III

<tce5tn$1di3$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108054&group=sci.math#108054

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: Wed, 3 Aug 2022 10:57:42 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tce5tn$1di3$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com>
<664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com>
<8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com>
<edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com>
<55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com>
<4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com>
<d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com>
<29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
<84f0f49a-8da8-42f4-8772-23c31060eba8n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="46659"; 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 - Wed, 3 Aug 2022 15:57 UTC

On 8/3/2022 10:33 AM, WM wrote:
> William schrieb am Mittwoch, 3. August 2022 um 17:22:57 UTC+2:
>> On Wednesday, August 3, 2022 at 11:14:37 AM UTC-3, WM wrote:
>
>>>> ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
>>>>
>>>> This is trivial as ℕ_def is finite.
>>> ℕ_def is finite
>> correct
>>> without a fixed last element however.
>> Piffle.
>
> Then define the last element.

which set consisting of ℕ_def elements are you talking about ?

>
>>> Many call it potentially infinite, that is it can be expanded without limit.
>> Note that even if we accept the fact that ℕ_def changes, it changes into something finite so
>> ∩({E(k) : k ∈ ℕ\ ℕ_def}) = { }
>> is "always" true (ℕ_def "always" has a last element).
>
> Yes. That is the property of potential infinity. But if you think to know the last element, then it is no longer the last element.

so, do you gather mankind into a circle and ask if they think they know the last element ?

>
>>> Let us call them numbers which cannot be written down.
>> Nope, there are many properties of "dark numbers" that do not hold for numbers which cannot be written down. (E.g. a "dark number"
>> is not connected to 1 by a finite number of successor operations)...
>
> You cannot know it for unwritable numbers.

WRONG.

the properties of unwritable numbers are listed here =>

>
>>> They may have other properties of natural numbers. But we cannot know.
>> Of course we can There are many ways, e.g. induction, to know that a number which does not have the property "can be written down", has other properties.
>
> Many.

Wrong.

>
> Regards, WM

Re: Natural numbers and vases III

<tce6hh$2av8v$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108055&group=sci.math#108055

copy link Newsgroups: sci.math

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 03 Aug 2022 12:08:03 -0400
Organization: Peripheral Visions
Lines: 6
Message-ID: <tce6hh$2av8v$1@dont-email.me>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com> <55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com> <2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com> <b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com> <ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com> <bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com> <39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com> <bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com> <537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 3 Aug 2022 16:08:17 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="e3e3056cca9516c0261fc2c686c51139";
logging-data="2456863"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/dF9EsJFCbU5ybheH9qVBZ3jglJG9Rn80="
Cancel-Lock: sha1:mPTRUdg8AueJ+HJVOKSRc4N2nwE=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

by: FromTheRafters - Wed, 3 Aug 2022 16:08 UTC

Re: Natural numbers and vases III

<9b572c29-d29a-4c3d-93e5-8ccced75fec1n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108058&group=sci.math#108058

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:21e2:b0:477:a3f:35c0 with SMTP id p2-20020a05621421e200b004770a3f35c0mr3606916qvj.66.1659545400440;
Wed, 03 Aug 2022 09:50:00 -0700 (PDT)
X-Received: by 2002:a05:6870:831a:b0:10d:bfae:cf3d with SMTP id
p26-20020a056870831a00b0010dbfaecf3dmr2326120oae.7.1659545400123; Wed, 03 Aug
2022 09:50:00 -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: Wed, 3 Aug 2022 09:49:59 -0700 (PDT)
In-Reply-To: <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@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>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <9b572c29-d29a-4c3d-93e5-8ccced75fec1n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Wed, 03 Aug 2022 16:50:00 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6033

by: Fritz Feldhase - Wed, 3 Aug 2022 16:49 UTC

On Wednesday, August 3, 2022 at 4:14:37 PM UTC+2, WM wrote:

The set

> ℕ_def is finite without a fixed last element however.

That's just nonsensical mumbo-jumbo.

Hint: If IN_def c IN is finite (and not empty) then it has a "certain" last element, this last element is called _the maximum of IN_def_, dumbo.

> Many call it potentially infinite

NO ONE *** EXCEPT YOU *** calls it "potentially infinite", YOU PSYCHOTIC LIAR!

> that is it can be expanded without limit.

Hint: If a !e A, then A u {a} =/= A for any set A.

Sets DON'T GROW.

And now to something completely different:

"Dark numbers"

> Let us call them numbers which cannot

ACTUALLY

> be written down [using, say, the unary numeral system --FF]

Why do you think that this an important feature of a natural number?

Seems that you (like a real psychtic) identify objects with their names.

Re: Natural numbers and vases III

<7cbcf4c4-b3bd-40a5-923c-dff731b92b43n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108059&group=sci.math#108059

copy link Newsgroups: sci.math

X-Received: by 2002:a05:622a:58b:b0:31f:407e:9e43 with SMTP id c11-20020a05622a058b00b0031f407e9e43mr22360957qtb.258.1659546502020;
Wed, 03 Aug 2022 10:08:22 -0700 (PDT)
X-Received: by 2002:a05:6870:c598:b0:108:b7e2:ac8 with SMTP id
ba24-20020a056870c59800b00108b7e20ac8mr2380835oab.1.1659546501731; Wed, 03
Aug 2022 10:08:21 -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: Wed, 3 Aug 2022 10:08:21 -0700 (PDT)
In-Reply-To: <2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@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>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <7cbcf4c4-b3bd-40a5-923c-dff731b92b43n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Wed, 03 Aug 2022 17:08:22 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6231

by: Fritz Feldhase - Wed, 3 Aug 2022 17:08 UTC

On Wednesday, August 3, 2022 at 5:22:57 PM UTC+2, William wrote:

> Note that even if we accept the fact that ℕ_def changes, it [...]

Hint: "sets are fixed they do not change" (Sergio)

Indeed.

Hint: If a !e ℕ_def then ℕ_def u {a} =/= N_def.

In the same way, ifa !e ℕ_def then ℕ_def \ {a} =/= N_def.

Gut that, dumbo?

Sets don't GROW or SHRINK.

Actually, sets are "specified" ("defined") by there elements. If the term "N_def" refers to a certain set IN A CERTAIN CONTEXT, then you should not adopt "IN_def" to refer to a different set IN THE SAME CONTEXT. This will lead to inconsistencies. (In the context of math/logic this holds for names/terms in general.)

This means: If (in a certain context) you call a certain set which does not contain the element /a/ "N_def". You should not call a set which DOES contain /a/ as an element "N_def" too (in the same context).

After all, this would allow to derive "~(a e N_def) & a e N_def" - a contradiction.

Re: Natural numbers and vases III

<2396eccd-6d57-4e79-86ff-f2458c850178n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108060&group=sci.math#108060

copy link Newsgroups: sci.math

X-Received: by 2002:a05:620a:1981:b0:6b5:cccf:62e1 with SMTP id bm1-20020a05620a198100b006b5cccf62e1mr18352721qkb.376.1659546651430;
Wed, 03 Aug 2022 10:10:51 -0700 (PDT)
X-Received: by 2002:a05:6870:14d0:b0:10e:5961:a12f with SMTP id
l16-20020a05687014d000b0010e5961a12fmr2294908oab.298.1659546651191; Wed, 03
Aug 2022 10:10:51 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 3 Aug 2022 10:10:51 -0700 (PDT)
In-Reply-To: <2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@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>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <2396eccd-6d57-4e79-86ff-f2458c850178n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Wed, 03 Aug 2022 17:10:51 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6231

by: Fritz Feldhase - Wed, 3 Aug 2022 17:10 UTC

On Wednesday, August 3, 2022 at 5:22:57 PM UTC+2, William wrote:

> Note that even if we accept [...] that ℕ_def changes, it [...]

Hint: "sets are fixed they do not change" (Sergio)

Indeed!

Hint: If a !e ℕ_def then ℕ_def u {a} =/= N_def.

In the same way, if a e ℕ_def then ℕ_def \ {a} =/= N_def.

Gut that, dumbo?

Sets don't GROW or SHRINK.

After all, this would allow to derive "~(a e N_def) & a e N_def" - a contradiction.

Re: Natural numbers and vases III

<21072626-5173-420f-a998-87dce694f263n@googlegroups.com>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=108061&group=sci.math#108061

copy link Newsgroups: sci.math

X-Received: by 2002:a05:6214:4017:b0:476:6229:bbf8 with SMTP id kd23-20020a056214401700b004766229bbf8mr16384323qvb.14.1659547103737;
Wed, 03 Aug 2022 10:18:23 -0700 (PDT)
X-Received: by 2002:a05:6830:2b28:b0:632:9516:bda5 with SMTP id
l40-20020a0568302b2800b006329516bda5mr4413958otv.382.1659547103510; Wed, 03
Aug 2022 10:18:23 -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: Wed, 3 Aug 2022 10:18:23 -0700 (PDT)
In-Reply-To: <2396eccd-6d57-4e79-86ff-f2458c850178n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=129.173.240.65; posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4
NNTP-Posting-Host: 129.173.240.65
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<1097840b-99c5-4bbf-a49c-5eaf33ff49b8n@googlegroups.com> <b7abbb63-3cc0-4009-a207-0b98e558e5f4n@googlegroups.com>
<15ab785e-8034-40bd-8c3f-2564407034edn@googlegroups.com> <107890fc-399f-46ed-88cf-c220b3940b99n@googlegroups.com>
<103fa899-4678-453c-94e4-011d89c3e94an@googlegroups.com> <01c579e1-60ed-499c-8294-069f117dc653n@googlegroups.com>
<ef2efaf0-050e-4801-83b0-92a37dedf903n@googlegroups.com> <4ed25630-bafc-445f-8ecb-e54a3f0841aen@googlegroups.com>
<5930923a-bf28-4af9-a807-2da5c74f2b1dn@googlegroups.com> <c9870e59-302d-4ad0-b930-73846d7ef5d7n@googlegroups.com>
<8a852e9e-0161-4b33-ba2d-00384ccfc7acn@googlegroups.com> <bc24558f-a8b7-4709-ae95-2c2a4634b23en@googlegroups.com>
<ad58ffff-cff9-4e1f-bd47-6096744ab370n@googlegroups.com> <4a9baad9-73d4-4ec0-924c-7b9686288be4n@googlegroups.com>
<5afd83ed-7b36-4639-a2b9-03d95293efcen@googlegroups.com> <b4c6ae72-9dc4-4bc7-82f5-40b88aaed2f0n@googlegroups.com>
<b70c52d1-6552-42f0-b875-0e570fed98dbn@googlegroups.com> <ab9f48dc-cc8c-4ecf-9929-a0e8739c2295n@googlegroups.com>
<cd28be3e-0da8-401f-bfa5-6e17e6da6d13n@googlegroups.com> <cbce4d5b-b8d5-43f2-9067-9683bb7850a8n@googlegroups.com>
<f9771698-918e-4b8a-ada1-716f142c2ca5n@googlegroups.com> <32394cc2-1d4f-4b17-b5e5-17dc91b6edfcn@googlegroups.com>
<0057edf9-0cc3-4ca7-a333-e8ef12ffbc9bn@googlegroups.com> <41e9407e-f545-4fc7-85c3-4fcf55249d7dn@googlegroups.com>
<9f0990e3-3396-4c6c-8c73-0cefb974a004n@googlegroups.com> <e91b802b-7fd7-42a6-b3b8-d9ffcb72af5fn@googlegroups.com>
<3aba40f4-c8ab-4e6d-9a91-53ca42165833n@googlegroups.com> <71df4106-30e8-4fc0-b959-41d8435fe557n@googlegroups.com>
<f2f08de0-701d-48c7-a093-412cf5a19f63n@googlegroups.com> <1f67bc11-4d32-4533-aab3-5d2156e99f45n@googlegroups.com>
<4c4d284f-5d87-40f8-b7cf-de2adc088c59n@googlegroups.com> <21112937-f642-4503-88d7-5da59431f344n@googlegroups.com>
<ad13089a-8969-439d-98f2-e1399a701909n@googlegroups.com> <c63ca417-364e-4be4-ba31-85129c7f89f8n@googlegroups.com>
<64e54d74-93eb-46b8-beda-e8c0bdc8a3a8n@googlegroups.com> <cedcd13f-8b89-4995-9306-3b4919a27b64n@googlegroups.com>
<a7577f83-da6d-4a4e-9c8e-56d2a27aa9een@googlegroups.com> <aedfb1b3-8d9c-4348-bf3c-0ddcc1095502n@googlegroups.com>
<e8ba1d81-c22c-457d-8ca2-95a155796fb2n@googlegroups.com> <8da6b9eb-efd9-465e-95d0-2cf611d6a05an@googlegroups.com>
<4e410a35-ddcd-43e0-bbd5-f2f1b13e9f84n@googlegroups.com> <e17a9d55-ab57-4f2b-9d64-21959a0924dan@googlegroups.com>
<ceaed9e5-c74b-4141-bca6-020a5e111367n@googlegroups.com> <458c729a-8d62-4704-ae76-bfaa19a60f4en@googlegroups.com>
<bcdae2c0-6b7c-41e9-aac5-7e171cb875e9n@googlegroups.com> <061b31bc-bcbf-457f-ad06-51699c853d14n@googlegroups.com>
<af742811-233d-49c6-bf7e-820d3e4f963bn@googlegroups.com> <09b5e743-9635-44e2-82eb-8bfcfc85c6d7n@googlegroups.com>
<cc73e70c-5b0a-42ac-b40a-3dc9a7f9daa8n@googlegroups.com> <3e10335c-8311-4821-bdf6-a6e0e551d423n@googlegroups.com>
<6b8e2fb7-e213-4b86-ac63-2466d4174543n@googlegroups.com> <eb026071-5cf6-4f92-9b07-2d4fae7f11c6n@googlegroups.com>
<55b763ab-12c3-47ed-a17f-59220ff76da6n@googlegroups.com> <d94da021-4874-4920-b101-06cf2a697753n@googlegroups.com>
<2ef71b08-72e5-4855-9664-fd37ab110615n@googlegroups.com> <664cb6fe-940a-4df1-b9c8-f538e3682464n@googlegroups.com>
<b07c4e50-6730-46df-aa5f-3f597a79cb0an@googlegroups.com> <8aa2088c-a26d-48ed-a8ef-512eeb07a404n@googlegroups.com>
<ab5b3807-f769-493a-a879-91341ac3584fn@googlegroups.com> <edd2807f-934f-4e92-b64f-7b25c819345en@googlegroups.com>
<bb98ff3b-17e8-45f0-9e1d-aa20cafe6bf5n@googlegroups.com> <55dc4132-b057-46f4-a763-794f0df27963n@googlegroups.com>
<39f99674-ba0f-4dd8-88b3-c8bbcf93cdb5n@googlegroups.com> <4b477578-942e-4e43-a193-9b43e97d6a64n@googlegroups.com>
<bed60254-3d76-4b67-9cd1-2fdf7abf2642n@googlegroups.com> <d2beedd3-bec2-4785-a474-67967e335a64n@googlegroups.com>
<537c9edf-f3c3-40bb-94ee-f770ec707594n@googlegroups.com> <29f4db0e-bc2e-47e4-8054-d4ffcdc55dc4n@googlegroups.com>
<2df78f92-52c1-4fa7-901a-ce4cd80eedf3n@googlegroups.com> <2396eccd-6d57-4e79-86ff-f2458c850178n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <21072626-5173-420f-a998-87dce694f263n@googlegroups.com>
Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Wed, 03 Aug 2022 17:18:23 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 6547

by: Gus Gassmann - Wed, 3 Aug 2022 17:18 UTC

On Wednesday, 3 August 2022 at 14:10:56 UTC-3, Fritz Feldhase wrote:
> On Wednesday, August 3, 2022 at 5:22:57 PM UTC+2, William wrote:
>
> > Note that even if we accept [...] that ℕ_def changes, it [...]
>
> Hint: "sets are fixed they do not change" (Sergio)
>
> Indeed!
>
> Hint: If a !e ℕ_def then ℕ_def u {a} =/= N_def.
>
> In the same way, if a e ℕ_def then ℕ_def \ {a} =/= N_def.
>
> Gut that, dumbo?
>
> Sets don't GROW or SHRINK.
>
> Actually, sets are "specified" ("defined") by there elements. If the term "N_def" refers to a certain set IN A CERTAIN CONTEXT, then you should not adopt "IN_def" to refer to a different set IN THE SAME CONTEXT. This will lead to inconsistencies. (In the context of math/logic this holds for names/terms in general.)
>
> This means: If (in a certain context) you call a certain set which does not contain the element /a/ "N_def". You should not call a set which DOES contain /a/ as an element "N_def" too (in the same context).
>
> After all, this would allow to derive "~(a e N_def) & a e N_def" - a contradiction.

But isn't such an "inconsistency" exactly what he is looking for? (Please don't hit me...)

I have a very small mind and must live with it. -- E. Dijkstra

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

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

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