X-Received: by 2002:a5d:64e9:0:b0:21b:c450:596f with SMTP id g9-20020a5d64e9000000b0021bc450596fmr6688660wri.35.1656568357381;
Wed, 29 Jun 2022 22:52:37 -0700 (PDT)
X-Received: by 2002:a05:6870:b617:b0:f5:d766:1b70 with SMTP id
cm23-20020a056870b61700b000f5d7661b70mr5474832oab.80.1656568356802; Wed, 29
Jun 2022 22:52:36 -0700 (PDT)
Path: i2pn2.org!i2pn.org!paganini.bofh.team!pasdenom.info!nntpfeed.proxad.net!proxad.net!feeder1-2.proxad.net!209.85.128.87.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 29 Jun 2022 22:52:36 -0700 (PDT)
In-Reply-To: <3c5e23ce-ab3b-4a6d-bf92-11570bbf712en@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.136.72.131; posting-account=9KdpAQoAAAAHk6UQCkS1dsKOLsVDFEUN
NNTP-Posting-Host: 79.136.72.131
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<8c3ae4ce-391d-48ec-8a83-77dd06e9721bn@googlegroups.com> <8c7fdce2-8901-48cd-8b08-3a720d2cae64n@googlegroups.com>
<1524b86f-50c5-432f-b2fe-42a347595755n@googlegroups.com> <70534b9c-d306-48c3-8c09-16eb0269e1c2n@googlegroups.com>
<eec33742-d59e-4f36-bbf8-6ded003d6422n@googlegroups.com> <0860c7f5-9c35-4ff5-9c12-ff14c8a1bb6bn@googlegroups.com>
<1a5a898b-dc9c-4948-9aa6-3231dcf06c15n@googlegroups.com> <237da8ab-8bec-489c-bbbc-c1a43d64bf6an@googlegroups.com>
<c952a918-bf4f-4c9c-8c6c-34bb98452758n@googlegroups.com> <858b03d6-fd8e-45f0-967e-8663b5d6cc47n@googlegroups.com>
<94779ba4-ee8c-43eb-86c8-44b2a253d2e2n@googlegroups.com> <8d2232cc-ad35-460d-90da-80c0deef6847n@googlegroups.com>
<fd833c8d-922e-468f-881c-a33e721e22a2n@googlegroups.com> <a17c74e3-e3a9-4e5d-88a5-8d4f460a2c32n@googlegroups.com>
<f1d6be67-cfc2-4808-882f-fbd23ecde1b1n@googlegroups.com> <849a4540-610e-40c3-90e8-8a1e69ce276en@googlegroups.com>
<t8m7qc$dba$1@gioia.aioe.org> <f18ec10d-8f6d-4b64-a949-926f6479e2ddn@googlegroups.com>
<5ccfc941-be4b-49bd-84b5-69e650cf5706n@googlegroups.com> <3061b621-c848-4fe5-accc-457f5596b4ebn@googlegroups.com>
<8bbc710e-cefa-451e-a57d-9822934a31c4n@googlegroups.com> <c11a3e07-2047-467b-aefa-94b77714f0f9n@googlegroups.com>
<a5d45cf4-305f-4780-aff5-9ef65dd7c1ben@googlegroups.com> <d85ec2bc-9ab1-484f-a444-2868b275b9bbn@googlegroups.com>
<e0778347-ea90-48fb-9dad-1136cdfacbean@googlegroups.com> <02f9d029-1efd-4cad-a7d9-ca8e4d54526an@googlegroups.com>
<05792425-c7de-4a15-b567-35cdf75a1447n@googlegroups.com> <0c3af4fe-5ac9-4389-b83a-0d7d714cf423n@googlegroups.com>
<ca2e9f41-05db-49b7-80a8-5c59f8905ccfn@googlegroups.com> <dcfd2a30-f0b5-4841-b2c6-a14511b8ae34n@googlegroups.com>
<c932be95-f8c4-4245-bf27-d6522a5edb46n@googlegroups.com> <e43830e1-71f1-4b10-8420-6720ddac66dcn@googlegroups.com>
<5db80b1f-578d-4d62-beb4-e32d1d1404f4n@googlegroups.com> <23193bfc-e393-4499-944b-0fbd07c42356n@googlegroups.com>
<2925c9b7-e64c-4380-b634-bbd29f3c7553n@googlegroups.com> <6da43a6b-7707-4c22-a7a4-3fdf304ab0c5n@googlegroups.com>
<18ef0ffb-9c04-49da-9265-ded1376715adn@googlegroups.com> <2cba7a40-ea9c-4d26-b93c-e6ae58803f5bn@googlegroups.com>
<4c858b67-ab0d-42d9-969c-7641c4954a13n@googlegroups.com> <58983fc6-2e05-4eb9-8321-9f46a7772d65n@googlegroups.com>
<8535d7b0-0ce1-45bb-882c-559c43d0038bn@googlegroups.com> <ff5c92e2-1b45-4e21-a85d-ca61fb49cc17n@googlegroups.com>
<83c2688a-016f-4316-808f-de346bd90004n@googlegroups.com> <ad1183b1-2618-4908-809f-ae289f91827en@googlegroups.com>
<eddae54e-8391-483c-bb39-11e02d808d5bn@googlegroups.com> <b05f9d6a-c08b-4c1f-9d80-588b2bbcb9a0n@googlegroups.com>
<a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com> <20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com>
<518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com> <b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com>
<55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com> <78c20ccb-d7f2-43a9-a873-ffc3217b2488n@googlegroups.com>
<3c5e23ce-ab3b-4a6d-bf92-11570bbf712en@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <14e0ac0d-9f57-4a28-8e1d-ed79c11db4efn@googlegroups.com>
Subject: Re: Natural numbers and vases
From: zelos.ma...@gmail.com (zelos...@gmail.com)
Injection-Date: Thu, 30 Jun 2022 05:52:37 +0000
Content-Type: text/plain; charset="UTF-8"

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 30 Jun 2022 06:10:18 -0400
Organization: Peripheral Visions
Lines: 18
Message-ID: <t9jsqh$1s3q1$1@dont-email.me>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com> <b05f9d6a-c08b-4c1f-9d80-588b2bbcb9a0n@googlegroups.com> <a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com> <20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com> <518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com> <b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com> <55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com> <057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com> <49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com> <acacdddf-8ada-47f0-81a8-a1aec8cbb87bn@googlegroups.com> <c92c9a16-1eac-4bd4-8429-06a4362b0683n@googlegroups.com> <6c25c484-1d21-4063-a910-614213f92f57n@googlegroups.com> <8ab76c13-7130-40c2-b45b-4cec0623a135n@googlegroups.com> <66bc1dd1-4829-42da-b291-e0d514f3a834n@googlegroups.com> <ab9a3830-b7a4-4334-9794-3b6466137824n@googlegroups.com> <t9ief9$1hqkf$1@dont-email.me> <14f11ed4-09bb-41b6-a955-5b8c0316b6c8n@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: Thu, 30 Jun 2022 10:10:25 -0000 (UTC)
Injection-Info: reader01.eternal-september.org; posting-host="c2b42e66a36b18fac42afdbd4eb74946";
logging-data="1969985"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SqkwGnKEu6sjV0zkhagUDVPVoA2UFDfI="
Cancel-Lock: sha1:TrrZ0JTeXn8Yqm7wmycMnOjMuHs=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

X-Received: by 2002:a05:600c:154a:b0:3a1:70dd:9a12 with SMTP id f10-20020a05600c154a00b003a170dd9a12mr8824675wmg.70.1656597259452;
Thu, 30 Jun 2022 06:54:19 -0700 (PDT)
X-Received: by 2002:a05:6808:f92:b0:32f:33af:7234 with SMTP id
o18-20020a0568080f9200b0032f33af7234mr6565660oiw.99.1656597258917; Thu, 30
Jun 2022 06:54:18 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.misty.com!border2.nntp.dca1.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: Thu, 30 Jun 2022 06:54:18 -0700 (PDT)
In-Reply-To: <18a58686-098a-4d1b-957e-47d162f66c32n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:84b6:24b9:eced:a4e7:5283;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:84b6:24b9:eced:a4e7:5283
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<8c3ae4ce-391d-48ec-8a83-77dd06e9721bn@googlegroups.com> <8c7fdce2-8901-48cd-8b08-3a720d2cae64n@googlegroups.com>
<1524b86f-50c5-432f-b2fe-42a347595755n@googlegroups.com> <70534b9c-d306-48c3-8c09-16eb0269e1c2n@googlegroups.com>
<eec33742-d59e-4f36-bbf8-6ded003d6422n@googlegroups.com> <0860c7f5-9c35-4ff5-9c12-ff14c8a1bb6bn@googlegroups.com>
<1a5a898b-dc9c-4948-9aa6-3231dcf06c15n@googlegroups.com> <237da8ab-8bec-489c-bbbc-c1a43d64bf6an@googlegroups.com>
<c952a918-bf4f-4c9c-8c6c-34bb98452758n@googlegroups.com> <858b03d6-fd8e-45f0-967e-8663b5d6cc47n@googlegroups.com>
<94779ba4-ee8c-43eb-86c8-44b2a253d2e2n@googlegroups.com> <8d2232cc-ad35-460d-90da-80c0deef6847n@googlegroups.com>
<fd833c8d-922e-468f-881c-a33e721e22a2n@googlegroups.com> <a17c74e3-e3a9-4e5d-88a5-8d4f460a2c32n@googlegroups.com>
<f1d6be67-cfc2-4808-882f-fbd23ecde1b1n@googlegroups.com> <849a4540-610e-40c3-90e8-8a1e69ce276en@googlegroups.com>
<t8m7qc$dba$1@gioia.aioe.org> <f18ec10d-8f6d-4b64-a949-926f6479e2ddn@googlegroups.com>
<5ccfc941-be4b-49bd-84b5-69e650cf5706n@googlegroups.com> <3061b621-c848-4fe5-accc-457f5596b4ebn@googlegroups.com>
<8bbc710e-cefa-451e-a57d-9822934a31c4n@googlegroups.com> <c11a3e07-2047-467b-aefa-94b77714f0f9n@googlegroups.com>
<a5d45cf4-305f-4780-aff5-9ef65dd7c1ben@googlegroups.com> <d85ec2bc-9ab1-484f-a444-2868b275b9bbn@googlegroups.com>
<e0778347-ea90-48fb-9dad-1136cdfacbean@googlegroups.com> <02f9d029-1efd-4cad-a7d9-ca8e4d54526an@googlegroups.com>
<05792425-c7de-4a15-b567-35cdf75a1447n@googlegroups.com> <0c3af4fe-5ac9-4389-b83a-0d7d714cf423n@googlegroups.com>
<ca2e9f41-05db-49b7-80a8-5c59f8905ccfn@googlegroups.com> <dcfd2a30-f0b5-4841-b2c6-a14511b8ae34n@googlegroups.com>
<c932be95-f8c4-4245-bf27-d6522a5edb46n@googlegroups.com> <e43830e1-71f1-4b10-8420-6720ddac66dcn@googlegroups.com>
<5db80b1f-578d-4d62-beb4-e32d1d1404f4n@googlegroups.com> <23193bfc-e393-4499-944b-0fbd07c42356n@googlegroups.com>
<2925c9b7-e64c-4380-b634-bbd29f3c7553n@googlegroups.com> <6da43a6b-7707-4c22-a7a4-3fdf304ab0c5n@googlegroups.com>
<18ef0ffb-9c04-49da-9265-ded1376715adn@googlegroups.com> <2cba7a40-ea9c-4d26-b93c-e6ae58803f5bn@googlegroups.com>
<4c858b67-ab0d-42d9-969c-7641c4954a13n@googlegroups.com> <58983fc6-2e05-4eb9-8321-9f46a7772d65n@googlegroups.com>
<8535d7b0-0ce1-45bb-882c-559c43d0038bn@googlegroups.com> <ff5c92e2-1b45-4e21-a85d-ca61fb49cc17n@googlegroups.com>
<83c2688a-016f-4316-808f-de346bd90004n@googlegroups.com> <ad1183b1-2618-4908-809f-ae289f91827en@googlegroups.com>
<eddae54e-8391-483c-bb39-11e02d808d5bn@googlegroups.com> <b05f9d6a-c08b-4c1f-9d80-588b2bbcb9a0n@googlegroups.com>
<a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com> <20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com>
<518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com> <b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com>
<55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com> <057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com>
<49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com> <b9348d29-b2d5-48b1-9c04-040a1bcaa7a7n@googlegroups.com>
<4f2ca2c0-86d6-4b88-9d86-44a14ef10e2bn@googlegroups.com> <2ccc865d-16c0-4a49-9943-d8f133273f35n@googlegroups.com>
<e35cd52f-3a06-4d41-8707-295f849877dbn@googlegroups.com> <7460d54b-c243-4516-957f-f02ecc4c25f5n@googlegroups.com>
<5225b55a-9ac3-4596-be42-384068d6ce6dn@googlegroups.com> <6e3a0e09-5d21-4774-b39e-6ad04d62fb67n@googlegroups.com>
<b96b087a-e477-46c3-90ba-9a01337888bbn@googlegroups.com> <486f1ef4-a7fa-455b-9a48-3453806482b3n@googlegroups.com>
<e93d74f3-08c5-4ffa-b15f-1a6949c9c0fbn@googlegroups.com> <c95bae54-1330-4273-98d3-b8c7742f3346n@googlegroups.com>
<4cffc59c-f607-4817-bd48-9285f251a8f7n@googlegroups.com> <18a58686-098a-4d1b-957e-47d162f66c32n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <de94233a-ea5d-42b0-8599-b0adc5fe52b9n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Thu, 30 Jun 2022 13:54:19 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 17

X-Received: by 2002:a05:6000:695:b0:21a:3a1a:7b60 with SMTP id bo21-20020a056000069500b0021a3a1a7b60mr8384753wrb.441.1656597606994;
Thu, 30 Jun 2022 07:00:06 -0700 (PDT)
X-Received: by 2002:a05:6870:b617:b0:f5:d766:1b70 with SMTP id
cm23-20020a056870b61700b000f5d7661b70mr6647327oab.80.1656597606491; Thu, 30
Jun 2022 07:00:06 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.128.88.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Thu, 30 Jun 2022 07:00:06 -0700 (PDT)
In-Reply-To: <t9jsqh$1s3q1$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7730:84b6:24b9:eced:a4e7:5283;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7730:84b6:24b9:eced:a4e7:5283
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<b05f9d6a-c08b-4c1f-9d80-588b2bbcb9a0n@googlegroups.com> <a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com>
<20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com> <518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com>
<b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com> <55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com>
<057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com> <49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com>
<acacdddf-8ada-47f0-81a8-a1aec8cbb87bn@googlegroups.com> <c92c9a16-1eac-4bd4-8429-06a4362b0683n@googlegroups.com>
<6c25c484-1d21-4063-a910-614213f92f57n@googlegroups.com> <8ab76c13-7130-40c2-b45b-4cec0623a135n@googlegroups.com>
<66bc1dd1-4829-42da-b291-e0d514f3a834n@googlegroups.com> <ab9a3830-b7a4-4334-9794-3b6466137824n@googlegroups.com>
<t9ief9$1hqkf$1@dont-email.me> <14f11ed4-09bb-41b6-a955-5b8c0316b6c8n@googlegroups.com>
<t9jsqh$1s3q1$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <8a9019ad-f119-40b5-a359-119d5ac07f9dn@googlegroups.com>
Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Thu, 30 Jun 2022 14:00:06 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

X-Received: by 2002:adf:f503:0:b0:21a:3d9c:b355 with SMTP id q3-20020adff503000000b0021a3d9cb355mr8348732wro.623.1656598820199;
Thu, 30 Jun 2022 07:20:20 -0700 (PDT)
X-Received: by 2002:a05:6830:25d0:b0:617:95f:9f5a with SMTP id
d16-20020a05683025d000b00617095f9f5amr3193513otu.369.1656598819541; Thu, 30
Jun 2022 07:20:19 -0700 (PDT)
Path: i2pn2.org!i2pn.org!paganini.bofh.team!pasdenom.info!nntpfeed.proxad.net!proxad.net!feeder1-2.proxad.net!209.85.128.87.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Thu, 30 Jun 2022 07:20:19 -0700 (PDT)
In-Reply-To: <de94233a-ea5d-42b0-8599-b0adc5fe52b9n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=156.57.37.70; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 156.57.37.70
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<8c3ae4ce-391d-48ec-8a83-77dd06e9721bn@googlegroups.com> <8c7fdce2-8901-48cd-8b08-3a720d2cae64n@googlegroups.com>
<1524b86f-50c5-432f-b2fe-42a347595755n@googlegroups.com> <70534b9c-d306-48c3-8c09-16eb0269e1c2n@googlegroups.com>
<eec33742-d59e-4f36-bbf8-6ded003d6422n@googlegroups.com> <0860c7f5-9c35-4ff5-9c12-ff14c8a1bb6bn@googlegroups.com>
<1a5a898b-dc9c-4948-9aa6-3231dcf06c15n@googlegroups.com> <237da8ab-8bec-489c-bbbc-c1a43d64bf6an@googlegroups.com>
<c952a918-bf4f-4c9c-8c6c-34bb98452758n@googlegroups.com> <858b03d6-fd8e-45f0-967e-8663b5d6cc47n@googlegroups.com>
<94779ba4-ee8c-43eb-86c8-44b2a253d2e2n@googlegroups.com> <8d2232cc-ad35-460d-90da-80c0deef6847n@googlegroups.com>
<fd833c8d-922e-468f-881c-a33e721e22a2n@googlegroups.com> <a17c74e3-e3a9-4e5d-88a5-8d4f460a2c32n@googlegroups.com>
<f1d6be67-cfc2-4808-882f-fbd23ecde1b1n@googlegroups.com> <849a4540-610e-40c3-90e8-8a1e69ce276en@googlegroups.com>
<t8m7qc$dba$1@gioia.aioe.org> <f18ec10d-8f6d-4b64-a949-926f6479e2ddn@googlegroups.com>
<5ccfc941-be4b-49bd-84b5-69e650cf5706n@googlegroups.com> <3061b621-c848-4fe5-accc-457f5596b4ebn@googlegroups.com>
<8bbc710e-cefa-451e-a57d-9822934a31c4n@googlegroups.com> <c11a3e07-2047-467b-aefa-94b77714f0f9n@googlegroups.com>
<a5d45cf4-305f-4780-aff5-9ef65dd7c1ben@googlegroups.com> <d85ec2bc-9ab1-484f-a444-2868b275b9bbn@googlegroups.com>
<e0778347-ea90-48fb-9dad-1136cdfacbean@googlegroups.com> <02f9d029-1efd-4cad-a7d9-ca8e4d54526an@googlegroups.com>
<05792425-c7de-4a15-b567-35cdf75a1447n@googlegroups.com> <0c3af4fe-5ac9-4389-b83a-0d7d714cf423n@googlegroups.com>
<ca2e9f41-05db-49b7-80a8-5c59f8905ccfn@googlegroups.com> <dcfd2a30-f0b5-4841-b2c6-a14511b8ae34n@googlegroups.com>
<c932be95-f8c4-4245-bf27-d6522a5edb46n@googlegroups.com> <e43830e1-71f1-4b10-8420-6720ddac66dcn@googlegroups.com>
<5db80b1f-578d-4d62-beb4-e32d1d1404f4n@googlegroups.com> <23193bfc-e393-4499-944b-0fbd07c42356n@googlegroups.com>
<2925c9b7-e64c-4380-b634-bbd29f3c7553n@googlegroups.com> <6da43a6b-7707-4c22-a7a4-3fdf304ab0c5n@googlegroups.com>
<18ef0ffb-9c04-49da-9265-ded1376715adn@googlegroups.com> <2cba7a40-ea9c-4d26-b93c-e6ae58803f5bn@googlegroups.com>
<4c858b67-ab0d-42d9-969c-7641c4954a13n@googlegroups.com> <58983fc6-2e05-4eb9-8321-9f46a7772d65n@googlegroups.com>
<8535d7b0-0ce1-45bb-882c-559c43d0038bn@googlegroups.com> <ff5c92e2-1b45-4e21-a85d-ca61fb49cc17n@googlegroups.com>
<83c2688a-016f-4316-808f-de346bd90004n@googlegroups.com> <ad1183b1-2618-4908-809f-ae289f91827en@googlegroups.com>
<eddae54e-8391-483c-bb39-11e02d808d5bn@googlegroups.com> <b05f9d6a-c08b-4c1f-9d80-588b2bbcb9a0n@googlegroups.com>
<a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com> <20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com>
<518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com> <b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com>
<55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com> <057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com>
<49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com> <b9348d29-b2d5-48b1-9c04-040a1bcaa7a7n@googlegroups.com>
<4f2ca2c0-86d6-4b88-9d86-44a14ef10e2bn@googlegroups.com> <2ccc865d-16c0-4a49-9943-d8f133273f35n@googlegroups.com>
<e35cd52f-3a06-4d41-8707-295f849877dbn@googlegroups.com> <7460d54b-c243-4516-957f-f02ecc4c25f5n@googlegroups.com>
<5225b55a-9ac3-4596-be42-384068d6ce6dn@googlegroups.com> <6e3a0e09-5d21-4774-b39e-6ad04d62fb67n@googlegroups.com>
<b96b087a-e477-46c3-90ba-9a01337888bbn@googlegroups.com> <486f1ef4-a7fa-455b-9a48-3453806482b3n@googlegroups.com>
<e93d74f3-08c5-4ffa-b15f-1a6949c9c0fbn@googlegroups.com> <c95bae54-1330-4273-98d3-b8c7742f3346n@googlegroups.com>
<4cffc59c-f607-4817-bd48-9285f251a8f7n@googlegroups.com> <18a58686-098a-4d1b-957e-47d162f66c32n@googlegroups.com>
<de94233a-ea5d-42b0-8599-b0adc5fe52b9n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <fa6b088d-ba61-43fb-9b72-6444bb808976n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Thu, 30 Jun 2022 14:20:20 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 30 Jun 2022 13:26:50 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t9kptb$3oj$1@gioia.aioe.org>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com>
<49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com>
<b9348d29-b2d5-48b1-9c04-040a1bcaa7a7n@googlegroups.com>
<4f2ca2c0-86d6-4b88-9d86-44a14ef10e2bn@googlegroups.com>
<2ccc865d-16c0-4a49-9943-d8f133273f35n@googlegroups.com>
<e35cd52f-3a06-4d41-8707-295f849877dbn@googlegroups.com>
<7460d54b-c243-4516-957f-f02ecc4c25f5n@googlegroups.com>
<5225b55a-9ac3-4596-be42-384068d6ce6dn@googlegroups.com>
<6e3a0e09-5d21-4774-b39e-6ad04d62fb67n@googlegroups.com>
<b96b087a-e477-46c3-90ba-9a01337888bbn@googlegroups.com>
<486f1ef4-a7fa-455b-9a48-3453806482b3n@googlegroups.com>
<e93d74f3-08c5-4ffa-b15f-1a6949c9c0fbn@googlegroups.com>
<c95bae54-1330-4273-98d3-b8c7742f3346n@googlegroups.com>
<4cffc59c-f607-4817-bd48-9285f251a8f7n@googlegroups.com>
<18a58686-098a-4d1b-957e-47d162f66c32n@googlegroups.com>
<de94233a-ea5d-42b0-8599-b0adc5fe52b9n@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="3859"; 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

Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 30 Jun 2022 13:32:08 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t9kq78$7nk$1@gioia.aioe.org>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<a3720ea1-1456-4c0c-978f-10809364116an@googlegroups.com>
<20a1c7a9-811a-40bf-8ef7-d70922d23801n@googlegroups.com>
<518e1fc9-3697-4293-a585-144e336d5529n@googlegroups.com>
<b26995b0-668e-4033-b587-ad0972d5eccbn@googlegroups.com>
<55c16f2f-539c-488d-93af-dbfb690730e1n@googlegroups.com>
<057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com>
<49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com>
<acacdddf-8ada-47f0-81a8-a1aec8cbb87bn@googlegroups.com>
<c92c9a16-1eac-4bd4-8429-06a4362b0683n@googlegroups.com>
<6c25c484-1d21-4063-a910-614213f92f57n@googlegroups.com>
<8ab76c13-7130-40c2-b45b-4cec0623a135n@googlegroups.com>
<66bc1dd1-4829-42da-b291-e0d514f3a834n@googlegroups.com>
<ab9a3830-b7a4-4334-9794-3b6466137824n@googlegroups.com>
<t9ief9$1hqkf$1@dont-email.me>
<14f11ed4-09bb-41b6-a955-5b8c0316b6c8n@googlegroups.com>
<t9jsqh$1s3q1$1@dont-email.me>
<8a9019ad-f119-40b5-a359-119d5ac07f9dn@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="7924"; 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

Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 30 Jun 2022 14:46:48 -0400
Organization: A noiseless patient Spider
Lines: 78
Message-ID: <9ac3ce5f-185a-1cc5-fb36-ef4f43242c54@att.net>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<057758d2-b333-48d5-ab97-8bacf1dcbaa3n@googlegroups.com>
<49d9262a-60a6-4532-9120-f6be61dde18cn@googlegroups.com>
<b9348d29-b2d5-48b1-9c04-040a1bcaa7a7n@googlegroups.com>
<4f2ca2c0-86d6-4b88-9d86-44a14ef10e2bn@googlegroups.com>
<2ccc865d-16c0-4a49-9943-d8f133273f35n@googlegroups.com>
<e35cd52f-3a06-4d41-8707-295f849877dbn@googlegroups.com>
<7460d54b-c243-4516-957f-f02ecc4c25f5n@googlegroups.com>
<5225b55a-9ac3-4596-be42-384068d6ce6dn@googlegroups.com>
<6e3a0e09-5d21-4774-b39e-6ad04d62fb67n@googlegroups.com>
<b96b087a-e477-46c3-90ba-9a01337888bbn@googlegroups.com>
<486f1ef4-a7fa-455b-9a48-3453806482b3n@googlegroups.com>
<e93d74f3-08c5-4ffa-b15f-1a6949c9c0fbn@googlegroups.com>
<c95bae54-1330-4273-98d3-b8c7742f3346n@googlegroups.com>
<4cffc59c-f607-4817-bd48-9285f251a8f7n@googlegroups.com>
<18a58686-098a-4d1b-957e-47d162f66c32n@googlegroups.com>
<de94233a-ea5d-42b0-8599-b0adc5fe52b9n@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: reader01.eternal-september.org; posting-host="3d7de308672ca3f51e93d411cea36cce";
logging-data="2101929"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/FuQXJZo1mMePQShsy4gV5eT5Y5v8ilzo="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.10.0
Cancel-Lock: sha1:6Rlf61FgiLjoDqtAklYiNMwFGuk=
Content-Language: en-US
In-Reply-To: <de94233a-ea5d-42b0-8599-b0adc5fe52b9n@googlegroups.com>