X-Received: by 2002:ac8:5fd0:0:b0:304:bd3d:d129 with SMTP id k16-20020ac85fd0000000b00304bd3dd129mr2185012qta.685.1654012423414;
Tue, 31 May 2022 08:53:43 -0700 (PDT)
X-Received: by 2002:a25:6b47:0:b0:65c:baf6:3924 with SMTP id
o7-20020a256b47000000b0065cbaf63924mr13499005ybm.485.1654012423258; Tue, 31
May 2022 08:53:43 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 08:53:43 -0700 (PDT)
In-Reply-To: <532fa42a-d34d-4f4d-9e85-ed1556ff9d16n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.170.162; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.170.162
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<af0e6d1b-b93a-48b0-b6db-501f95087564n@googlegroups.com> <16a4fb02-4ce0-4b85-94f2-1da4eec4bc27n@googlegroups.com>
<eb9e17d7-40bb-4d67-9201-9faa19302c16n@googlegroups.com> <34375b13-2fab-4927-b903-692b0798dbefn@googlegroups.com>
<0861ac88-84d8-48f0-831e-d5efe07c3ee2n@googlegroups.com> <f7ee355b-07d0-4b2a-82fb-c6477aab1232n@googlegroups.com>
<d6dd91c6-5756-4508-80a5-fd713d70351an@googlegroups.com> <d08db3bd-1624-4dd2-86b0-e5c336f2d907n@googlegroups.com>
<fc6a3664-b6cf-4cdd-9bc9-f6706575f51dn@googlegroups.com> <01d8dbb8-c6b6-4eac-a826-9d9217251a9fn@googlegroups.com>
<23ef8249-b7df-433f-974b-31b97f4db7bbn@googlegroups.com> <2314f69a-0262-4c26-9fc3-e708a567e196n@googlegroups.com>
<c442a802-2246-42cd-8f5e-2b4e40b631f0n@googlegroups.com> <9612dc60-7676-4417-9cd1-220e6d065132n@googlegroups.com>
<a6e7fe44-87f6-478d-a3e5-435f1d0461bcn@googlegroups.com> <be871dfb-288a-4b43-a8b1-2fa052b8edc1n@googlegroups.com>
<e610493d-5a8e-4055-a95c-0ad8568da48an@googlegroups.com> <c79a4186-dc4e-4cac-865e-6e7d45d586b1n@googlegroups.com>
<60955268-b979-4f46-89b3-97b373faa806n@googlegroups.com> <d6b21676-3dab-4097-87e4-8510cc520efen@googlegroups.com>
<4c053909-87ce-4285-991b-368c8b212b2dn@googlegroups.com> <5f31dc55-0a92-475d-8b13-4f6a871654bfn@googlegroups.com>
<a6b0f80c-9559-4508-9760-84313d7ecf10n@googlegroups.com> <feb0aa7f-69ef-4698-b25c-935aeb96d67bn@googlegroups.com>
<ef4a445e-de91-4271-8e2e-b2d3aeb50d81n@googlegroups.com> <4837804e-ee17-4804-80b4-0c17f00a4d7an@googlegroups.com>
<ef491fdd-6e20-4fea-8f84-497046dac5b3n@googlegroups.com> <01db1bca-c6fc-4ba8-be75-37ce679b070dn@googlegroups.com>
<fcd32c40-18c2-457d-8f71-e2d378bf3288n@googlegroups.com> <756a88cf-a3e6-4ad9-93dc-627eef357e8dn@googlegroups.com>
<9756fced-2bdf-4272-8801-b2654392c1f1n@googlegroups.com> <cb59dff5-96b9-4dd9-97d6-37edafce6ce1n@googlegroups.com>
<b5d8aee2-192b-4d12-ac63-a8ff320e4863n@googlegroups.com> <c46a3018-a3e1-4602-a4a9-7944a734e2b9n@googlegroups.com>
<79bf5344-9cad-4a6b-b14d-355828f5fa36n@googlegroups.com> <5482bad8-4c32-4ac4-bf4f-968e96c5159en@googlegroups.com>
<55d5c2fd-8c1d-4fd9-891f-2948b0a6081en@googlegroups.com> <137ba311-30ec-43bf-a78e-f46c1e412464n@googlegroups.com>
<435a423f-5c70-4349-ac0e-cb91b10c89a1n@googlegroups.com> <c8e83a2d-ca6f-4580-a232-38344b5f3141n@googlegroups.com>
<cbc1a821-f7d1-4b92-83c6-c01111f6ba4fn@googlegroups.com> <1260682a-990d-40da-aec4-ee194a95b07cn@googlegroups.com>
<60052711-3f3e-423e-bf83-9c2628aa7401n@googlegroups.com> <ac680fc3-78ef-476b-9e7a-513c848b4c94n@googlegroups.com>
<6a4c7b09-6de2-412e-8bf9-e17c1e6bf990n@googlegroups.com> <173c6ac0-13c7-42d5-8bf3-64e8f0fc0556n@googlegroups.com>
<447d479e-8fd1-4fb0-861b-da083da557den@googlegroups.com> <667344fe-c5e4-46ed-a129-2c41a380cfbbn@googlegroups.com>
<94ef4c02-445f-4258-856b-99453396509fn@googlegroups.com> <89eb596a-6480-44be-ab59-6d9be7a1ac03n@googlegroups.com>
<30096113-38b6-459b-96ce-17f8c87df610n@googlegroups.com> <a41e936d-7f27-4cf5-894c-43adb12278edn@googlegroups.com>
<3c503871-597b-4d9e-8184-68259c58b2a8n@googlegroups.com> <6fd21408-ab3c-4714-8213-48c455839334n@googlegroups.com>
<e145a374-18cc-4671-8325-2f8e50fce523n@googlegroups.com> <0a1a58b1-6d1d-4f01-ac00-0f2d6be020abn@googlegroups.com>
<8db140e2-bec7-479f-913a-b63c7b702f7bn@googlegroups.com> <bd266bcf-6197-4ec3-9784-098ec2605d6fn@googlegroups.com>
<7733ec3e-56f2-4b5c-964d-fb9e130c0bccn@googlegroups.com> <1611b520-8d07-474b-ad6f-a0e4d18eb996n@googlegroups.com>
<5f0a82ca-d1a8-44ee-9603-44787c624683n@googlegroups.com> <6ca7d142-8c2c-4e25-aca9-53ea0cd319c2n@googlegroups.com>
<5112d49b-03fe-4e53-bb4c-332d3ce272e7n@googlegroups.com> <57fa08b3-751e-4680-be7e-2632f96d0f48n@googlegroups.com>
<f1685be4-7ba3-43c2-b48c-d9c480d205cbn@googlegroups.com> <9614a5a5-94c1-4639-9334-85f5091164dfn@googlegroups.com>
<62fd07f5-3b15-42ab-804f-2817db3baa70n@googlegroups.com> <98bda7c3-63a8-459d-aa4e-d442ccd44427n@googlegroups.com>
<8bfc098d-8fad-4ee8-82a6-5dc18d912c89n@googlegroups.com> <c37630ee-12e0-4421-b8b0-55d3c3f04496n@googlegroups.com>
<23e46415-1bf1-4399-88fa-3e3ebe47efcan@googlegroups.com> <d768f058-126d-434a-9551-005344a6cf36n@googlegroups.com>
<2eed664f-4083-4c87-89e2-7a71219d7ffen@googlegroups.com> <b5470a4c-1fde-4b73-b8a1-66429f69f2b0n@googlegroups.com>
<1159ca4a-6452-4317-8367-d7ff155799d4n@googlegroups.com> <eabc9b91-3637-4ea8-b80d-25ae8d872a92n@googlegroups.com>
<bb08354f-1bd6-47c8-a630-2839f0ca3625n@googlegroups.com> <f1a5dfc3-ffdc-4fad-9737-461c80962075n@googlegroups.com>
<4310ea50-2f05-42f0-be3f-cb48e3175eb2n@googlegroups.com> <721ef121-7390-4772-be6a-986665480964n@googlegroups.com>
<06e0b912-a764-42c1-ad50-eb2c410d2dcen@googlegroups.com> <1fe9fe24-ef19-486d-b3c0-7743e6dab69bn@googlegroups.com>
<9d419dee-473d-493a-b099-044a2c4b783dn@googlegroups.com> <6b5eccf4-e9ed-4654-8ed4-1a00c5ff5f5en@googlegroups.com>
<3bd05f4a-3b2e-49b3-b7c7-7b05f2afae13n@googlegroups.com> <f81cc95e-7491-4704-8484-0399990dbddbn@googlegroups.com>
<f0ea98e1-fb57-4fc7-9b2e-fd74b9aaa04an@googlegroups.com> <b9453197-ef5a-4fe3-8cb0-76c3af5e9ae6n@googlegroups.com>
<d1436fb7-195b-418b-91bc-9305a3e710a7n@googlegroups.com> <95c178d8-c38f-4999-a5d5-0616d25392afn@googlegroups.com>
<d13957b7-104d-4a2d-b0e9-a7a03ec66b3cn@googlegroups.com> <24e77d9c-cad9-49f7-ac97-82db28d9692en@googlegroups.com>
<63debfaa-4e79-418e-9577-c3d4183a6f0bn@googlegroups.com> <58e48110-a7e2-4776-b1ed-978e6d240e2bn@googlegroups.com>
<97d27255-d796-4b1c-a30a-44226dba0c37n@googlegroups.com> <7d9f82cc-e322-468d-8deb-bcdbc8e11e3cn@googlegroups.com>
<f3bb9919-58cd-4915-8f3b-583968e299c5n@googlegroups.com> <6ece56a0-5d42-43d2-bf14-d3af90c8ba4dn@googlegroups.com>
<bcc065b7-9396-4fbf-a33a-1974cca890e3n@googlegroups.com> <532fa42a-d34d-4f4d-9e85-ed1556ff9d16n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Tue, 31 May 2022 15:53:43 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 7497

X-Received: by 2002:a05:622a:410:b0:2fb:be7b:68e6 with SMTP id n16-20020a05622a041000b002fbbe7b68e6mr24577075qtx.655.1654012538553;
Tue, 31 May 2022 08:55:38 -0700 (PDT)
X-Received: by 2002:a81:5305:0:b0:304:a8cb:9589 with SMTP id
h5-20020a815305000000b00304a8cb9589mr26151233ywb.2.1654012538341; Tue, 31 May
2022 08:55:38 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 08:55:38 -0700 (PDT)
In-Reply-To: <f3ec52aa-b308-928e-84fe-70fa2e298ace@att.net>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.205.4; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.205.4
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<725c42dd-3000-41bc-bdeb-b114c3d3de9cn@googlegroups.com> <94252f9a-0ced-1224-3b51-f79c9454dd05@att.net>
<12196cf5-a7ec-4297-9d1c-4e182a9ed9fbn@googlegroups.com> <e68a7682-8c0a-32eb-0f4a-2cff19e0c76f@att.net>
<0eedcd9e-f120-4151-a960-036acb36fafen@googlegroups.com> <37a4026a-46e1-cfbc-cdf6-2885d39eb4f4@att.net>
<19bcfc7c-5e49-4143-98cb-6253a3fb2412n@googlegroups.com> <1fbd8314-78bf-8437-cfb5-ddf782fcd7d5@att.net>
<f328880c-52f3-46f2-8ff5-1e2e2ff86592n@googlegroups.com> <c1e9d912-fc3f-0d1d-3e32-1f2a55d4463c@att.net>
<9e2f663c-7c97-4408-bab1-05a778f90901n@googlegroups.com> <0cadf616-d229-7a8a-7c89-4e4b7349703f@att.net>
<bd71bb8c-a9cc-4deb-a7ef-4faf950faecfn@googlegroups.com> <eba05ea8-58c8-2b48-969c-9989d8e0c457@att.net>
<fb3831a2-7ee8-4022-b4d3-332ba7184673n@googlegroups.com> <b8469877-db01-4387-23c7-99e45eaea0e4@att.net>
<d9f1fe53-859d-4afb-b1d7-773ec13ccfa3n@googlegroups.com> <f3ec52aa-b308-928e-84fe-70fa2e298ace@att.net>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <45dc0f00-d059-4617-ae3e-7faff45a9e21n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Tue, 31 May 2022 15:55:38 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2249

X-Received: by 2002:ac8:5c96:0:b0:2f9:3077:5cda with SMTP id r22-20020ac85c96000000b002f930775cdamr39271345qta.625.1654013130209;
Tue, 31 May 2022 09:05:30 -0700 (PDT)
X-Received: by 2002:a81:6d5:0:b0:300:58f2:118e with SMTP id
204-20020a8106d5000000b0030058f2118emr34430745ywg.78.1654013130018; Tue, 31
May 2022 09:05:30 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 09:05:29 -0700 (PDT)
In-Reply-To: <87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=79.206.205.4; posting-account=-75WZwoAAABL0f0-07Kn6tvNHWg7W9AE
NNTP-Posting-Host: 79.206.205.4
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<af0e6d1b-b93a-48b0-b6db-501f95087564n@googlegroups.com> <16a4fb02-4ce0-4b85-94f2-1da4eec4bc27n@googlegroups.com>
<eb9e17d7-40bb-4d67-9201-9faa19302c16n@googlegroups.com> <34375b13-2fab-4927-b903-692b0798dbefn@googlegroups.com>
<0861ac88-84d8-48f0-831e-d5efe07c3ee2n@googlegroups.com> <f7ee355b-07d0-4b2a-82fb-c6477aab1232n@googlegroups.com>
<d6dd91c6-5756-4508-80a5-fd713d70351an@googlegroups.com> <d08db3bd-1624-4dd2-86b0-e5c336f2d907n@googlegroups.com>
<fc6a3664-b6cf-4cdd-9bc9-f6706575f51dn@googlegroups.com> <01d8dbb8-c6b6-4eac-a826-9d9217251a9fn@googlegroups.com>
<23ef8249-b7df-433f-974b-31b97f4db7bbn@googlegroups.com> <2314f69a-0262-4c26-9fc3-e708a567e196n@googlegroups.com>
<c442a802-2246-42cd-8f5e-2b4e40b631f0n@googlegroups.com> <9612dc60-7676-4417-9cd1-220e6d065132n@googlegroups.com>
<a6e7fe44-87f6-478d-a3e5-435f1d0461bcn@googlegroups.com> <be871dfb-288a-4b43-a8b1-2fa052b8edc1n@googlegroups.com>
<e610493d-5a8e-4055-a95c-0ad8568da48an@googlegroups.com> <c79a4186-dc4e-4cac-865e-6e7d45d586b1n@googlegroups.com>
<60955268-b979-4f46-89b3-97b373faa806n@googlegroups.com> <d6b21676-3dab-4097-87e4-8510cc520efen@googlegroups.com>
<4c053909-87ce-4285-991b-368c8b212b2dn@googlegroups.com> <5f31dc55-0a92-475d-8b13-4f6a871654bfn@googlegroups.com>
<a6b0f80c-9559-4508-9760-84313d7ecf10n@googlegroups.com> <feb0aa7f-69ef-4698-b25c-935aeb96d67bn@googlegroups.com>
<ef4a445e-de91-4271-8e2e-b2d3aeb50d81n@googlegroups.com> <4837804e-ee17-4804-80b4-0c17f00a4d7an@googlegroups.com>
<ef491fdd-6e20-4fea-8f84-497046dac5b3n@googlegroups.com> <01db1bca-c6fc-4ba8-be75-37ce679b070dn@googlegroups.com>
<fcd32c40-18c2-457d-8f71-e2d378bf3288n@googlegroups.com> <756a88cf-a3e6-4ad9-93dc-627eef357e8dn@googlegroups.com>
<9756fced-2bdf-4272-8801-b2654392c1f1n@googlegroups.com> <cb59dff5-96b9-4dd9-97d6-37edafce6ce1n@googlegroups.com>
<b5d8aee2-192b-4d12-ac63-a8ff320e4863n@googlegroups.com> <c46a3018-a3e1-4602-a4a9-7944a734e2b9n@googlegroups.com>
<79bf5344-9cad-4a6b-b14d-355828f5fa36n@googlegroups.com> <5482bad8-4c32-4ac4-bf4f-968e96c5159en@googlegroups.com>
<55d5c2fd-8c1d-4fd9-891f-2948b0a6081en@googlegroups.com> <137ba311-30ec-43bf-a78e-f46c1e412464n@googlegroups.com>
<435a423f-5c70-4349-ac0e-cb91b10c89a1n@googlegroups.com> <c8e83a2d-ca6f-4580-a232-38344b5f3141n@googlegroups.com>
<cbc1a821-f7d1-4b92-83c6-c01111f6ba4fn@googlegroups.com> <1260682a-990d-40da-aec4-ee194a95b07cn@googlegroups.com>
<60052711-3f3e-423e-bf83-9c2628aa7401n@googlegroups.com> <ac680fc3-78ef-476b-9e7a-513c848b4c94n@googlegroups.com>
<6a4c7b09-6de2-412e-8bf9-e17c1e6bf990n@googlegroups.com> <173c6ac0-13c7-42d5-8bf3-64e8f0fc0556n@googlegroups.com>
<447d479e-8fd1-4fb0-861b-da083da557den@googlegroups.com> <667344fe-c5e4-46ed-a129-2c41a380cfbbn@googlegroups.com>
<94ef4c02-445f-4258-856b-99453396509fn@googlegroups.com> <89eb596a-6480-44be-ab59-6d9be7a1ac03n@googlegroups.com>
<30096113-38b6-459b-96ce-17f8c87df610n@googlegroups.com> <a41e936d-7f27-4cf5-894c-43adb12278edn@googlegroups.com>
<3c503871-597b-4d9e-8184-68259c58b2a8n@googlegroups.com> <6fd21408-ab3c-4714-8213-48c455839334n@googlegroups.com>
<e145a374-18cc-4671-8325-2f8e50fce523n@googlegroups.com> <0a1a58b1-6d1d-4f01-ac00-0f2d6be020abn@googlegroups.com>
<8db140e2-bec7-479f-913a-b63c7b702f7bn@googlegroups.com> <bd266bcf-6197-4ec3-9784-098ec2605d6fn@googlegroups.com>
<7733ec3e-56f2-4b5c-964d-fb9e130c0bccn@googlegroups.com> <1611b520-8d07-474b-ad6f-a0e4d18eb996n@googlegroups.com>
<5f0a82ca-d1a8-44ee-9603-44787c624683n@googlegroups.com> <6ca7d142-8c2c-4e25-aca9-53ea0cd319c2n@googlegroups.com>
<5112d49b-03fe-4e53-bb4c-332d3ce272e7n@googlegroups.com> <57fa08b3-751e-4680-be7e-2632f96d0f48n@googlegroups.com>
<f1685be4-7ba3-43c2-b48c-d9c480d205cbn@googlegroups.com> <9614a5a5-94c1-4639-9334-85f5091164dfn@googlegroups.com>
<62fd07f5-3b15-42ab-804f-2817db3baa70n@googlegroups.com> <98bda7c3-63a8-459d-aa4e-d442ccd44427n@googlegroups.com>
<8bfc098d-8fad-4ee8-82a6-5dc18d912c89n@googlegroups.com> <c37630ee-12e0-4421-b8b0-55d3c3f04496n@googlegroups.com>
<23e46415-1bf1-4399-88fa-3e3ebe47efcan@googlegroups.com> <d768f058-126d-434a-9551-005344a6cf36n@googlegroups.com>
<2eed664f-4083-4c87-89e2-7a71219d7ffen@googlegroups.com> <b5470a4c-1fde-4b73-b8a1-66429f69f2b0n@googlegroups.com>
<1159ca4a-6452-4317-8367-d7ff155799d4n@googlegroups.com> <eabc9b91-3637-4ea8-b80d-25ae8d872a92n@googlegroups.com>
<bb08354f-1bd6-47c8-a630-2839f0ca3625n@googlegroups.com> <f1a5dfc3-ffdc-4fad-9737-461c80962075n@googlegroups.com>
<4310ea50-2f05-42f0-be3f-cb48e3175eb2n@googlegroups.com> <721ef121-7390-4772-be6a-986665480964n@googlegroups.com>
<06e0b912-a764-42c1-ad50-eb2c410d2dcen@googlegroups.com> <1fe9fe24-ef19-486d-b3c0-7743e6dab69bn@googlegroups.com>
<9d419dee-473d-493a-b099-044a2c4b783dn@googlegroups.com> <6b5eccf4-e9ed-4654-8ed4-1a00c5ff5f5en@googlegroups.com>
<3bd05f4a-3b2e-49b3-b7c7-7b05f2afae13n@googlegroups.com> <f81cc95e-7491-4704-8484-0399990dbddbn@googlegroups.com>
<f0ea98e1-fb57-4fc7-9b2e-fd74b9aaa04an@googlegroups.com> <b9453197-ef5a-4fe3-8cb0-76c3af5e9ae6n@googlegroups.com>
<d1436fb7-195b-418b-91bc-9305a3e710a7n@googlegroups.com> <95c178d8-c38f-4999-a5d5-0616d25392afn@googlegroups.com>
<d13957b7-104d-4a2d-b0e9-a7a03ec66b3cn@googlegroups.com> <24e77d9c-cad9-49f7-ac97-82db28d9692en@googlegroups.com>
<63debfaa-4e79-418e-9577-c3d4183a6f0bn@googlegroups.com> <58e48110-a7e2-4776-b1ed-978e6d240e2bn@googlegroups.com>
<97d27255-d796-4b1c-a30a-44226dba0c37n@googlegroups.com> <7d9f82cc-e322-468d-8deb-bcdbc8e11e3cn@googlegroups.com>
<f3bb9919-58cd-4915-8f3b-583968e299c5n@googlegroups.com> <6ece56a0-5d42-43d2-bf14-d3af90c8ba4dn@googlegroups.com>
<bcc065b7-9396-4fbf-a33a-1974cca890e3n@googlegroups.com> <532fa42a-d34d-4f4d-9e85-ed1556ff9d16n@googlegroups.com>
<87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <9d46dcc7-4d5d-47b9-9318-abf9ac0c612an@googlegroups.com>
Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Tue, 31 May 2022 16:05:30 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 7518

X-Received: by 2002:a05:622a:108:b0:2fc:7ed3:a158 with SMTP id u8-20020a05622a010800b002fc7ed3a158mr22661928qtw.597.1654028348293;
Tue, 31 May 2022 13:19:08 -0700 (PDT)
X-Received: by 2002:a81:3602:0:b0:30d:6d92:19be with SMTP id
d2-20020a813602000000b0030d6d9219bemr1166900ywa.422.1654028348128; Tue, 31
May 2022 13:19:08 -0700 (PDT)
Path: i2pn2.org!i2pn.org!paganini.bofh.team!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 13:19:07 -0700 (PDT)
In-Reply-To: <87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:573c:1f2:a917:58fc:dc77;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:573c:1f2:a917:58fc:dc77
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<af0e6d1b-b93a-48b0-b6db-501f95087564n@googlegroups.com> <16a4fb02-4ce0-4b85-94f2-1da4eec4bc27n@googlegroups.com>
<eb9e17d7-40bb-4d67-9201-9faa19302c16n@googlegroups.com> <34375b13-2fab-4927-b903-692b0798dbefn@googlegroups.com>
<0861ac88-84d8-48f0-831e-d5efe07c3ee2n@googlegroups.com> <f7ee355b-07d0-4b2a-82fb-c6477aab1232n@googlegroups.com>
<d6dd91c6-5756-4508-80a5-fd713d70351an@googlegroups.com> <d08db3bd-1624-4dd2-86b0-e5c336f2d907n@googlegroups.com>
<fc6a3664-b6cf-4cdd-9bc9-f6706575f51dn@googlegroups.com> <01d8dbb8-c6b6-4eac-a826-9d9217251a9fn@googlegroups.com>
<23ef8249-b7df-433f-974b-31b97f4db7bbn@googlegroups.com> <2314f69a-0262-4c26-9fc3-e708a567e196n@googlegroups.com>
<c442a802-2246-42cd-8f5e-2b4e40b631f0n@googlegroups.com> <9612dc60-7676-4417-9cd1-220e6d065132n@googlegroups.com>
<a6e7fe44-87f6-478d-a3e5-435f1d0461bcn@googlegroups.com> <be871dfb-288a-4b43-a8b1-2fa052b8edc1n@googlegroups.com>
<e610493d-5a8e-4055-a95c-0ad8568da48an@googlegroups.com> <c79a4186-dc4e-4cac-865e-6e7d45d586b1n@googlegroups.com>
<60955268-b979-4f46-89b3-97b373faa806n@googlegroups.com> <d6b21676-3dab-4097-87e4-8510cc520efen@googlegroups.com>
<4c053909-87ce-4285-991b-368c8b212b2dn@googlegroups.com> <5f31dc55-0a92-475d-8b13-4f6a871654bfn@googlegroups.com>
<a6b0f80c-9559-4508-9760-84313d7ecf10n@googlegroups.com> <feb0aa7f-69ef-4698-b25c-935aeb96d67bn@googlegroups.com>
<ef4a445e-de91-4271-8e2e-b2d3aeb50d81n@googlegroups.com> <4837804e-ee17-4804-80b4-0c17f00a4d7an@googlegroups.com>
<ef491fdd-6e20-4fea-8f84-497046dac5b3n@googlegroups.com> <01db1bca-c6fc-4ba8-be75-37ce679b070dn@googlegroups.com>
<fcd32c40-18c2-457d-8f71-e2d378bf3288n@googlegroups.com> <756a88cf-a3e6-4ad9-93dc-627eef357e8dn@googlegroups.com>
<9756fced-2bdf-4272-8801-b2654392c1f1n@googlegroups.com> <cb59dff5-96b9-4dd9-97d6-37edafce6ce1n@googlegroups.com>
<b5d8aee2-192b-4d12-ac63-a8ff320e4863n@googlegroups.com> <c46a3018-a3e1-4602-a4a9-7944a734e2b9n@googlegroups.com>
<79bf5344-9cad-4a6b-b14d-355828f5fa36n@googlegroups.com> <5482bad8-4c32-4ac4-bf4f-968e96c5159en@googlegroups.com>
<55d5c2fd-8c1d-4fd9-891f-2948b0a6081en@googlegroups.com> <137ba311-30ec-43bf-a78e-f46c1e412464n@googlegroups.com>
<435a423f-5c70-4349-ac0e-cb91b10c89a1n@googlegroups.com> <c8e83a2d-ca6f-4580-a232-38344b5f3141n@googlegroups.com>
<cbc1a821-f7d1-4b92-83c6-c01111f6ba4fn@googlegroups.com> <1260682a-990d-40da-aec4-ee194a95b07cn@googlegroups.com>
<60052711-3f3e-423e-bf83-9c2628aa7401n@googlegroups.com> <ac680fc3-78ef-476b-9e7a-513c848b4c94n@googlegroups.com>
<6a4c7b09-6de2-412e-8bf9-e17c1e6bf990n@googlegroups.com> <173c6ac0-13c7-42d5-8bf3-64e8f0fc0556n@googlegroups.com>
<447d479e-8fd1-4fb0-861b-da083da557den@googlegroups.com> <667344fe-c5e4-46ed-a129-2c41a380cfbbn@googlegroups.com>
<94ef4c02-445f-4258-856b-99453396509fn@googlegroups.com> <89eb596a-6480-44be-ab59-6d9be7a1ac03n@googlegroups.com>
<30096113-38b6-459b-96ce-17f8c87df610n@googlegroups.com> <a41e936d-7f27-4cf5-894c-43adb12278edn@googlegroups.com>
<3c503871-597b-4d9e-8184-68259c58b2a8n@googlegroups.com> <6fd21408-ab3c-4714-8213-48c455839334n@googlegroups.com>
<e145a374-18cc-4671-8325-2f8e50fce523n@googlegroups.com> <0a1a58b1-6d1d-4f01-ac00-0f2d6be020abn@googlegroups.com>
<8db140e2-bec7-479f-913a-b63c7b702f7bn@googlegroups.com> <bd266bcf-6197-4ec3-9784-098ec2605d6fn@googlegroups.com>
<7733ec3e-56f2-4b5c-964d-fb9e130c0bccn@googlegroups.com> <1611b520-8d07-474b-ad6f-a0e4d18eb996n@googlegroups.com>
<5f0a82ca-d1a8-44ee-9603-44787c624683n@googlegroups.com> <6ca7d142-8c2c-4e25-aca9-53ea0cd319c2n@googlegroups.com>
<5112d49b-03fe-4e53-bb4c-332d3ce272e7n@googlegroups.com> <57fa08b3-751e-4680-be7e-2632f96d0f48n@googlegroups.com>
<f1685be4-7ba3-43c2-b48c-d9c480d205cbn@googlegroups.com> <9614a5a5-94c1-4639-9334-85f5091164dfn@googlegroups.com>
<62fd07f5-3b15-42ab-804f-2817db3baa70n@googlegroups.com> <98bda7c3-63a8-459d-aa4e-d442ccd44427n@googlegroups.com>
<8bfc098d-8fad-4ee8-82a6-5dc18d912c89n@googlegroups.com> <c37630ee-12e0-4421-b8b0-55d3c3f04496n@googlegroups.com>
<23e46415-1bf1-4399-88fa-3e3ebe47efcan@googlegroups.com> <d768f058-126d-434a-9551-005344a6cf36n@googlegroups.com>
<2eed664f-4083-4c87-89e2-7a71219d7ffen@googlegroups.com> <b5470a4c-1fde-4b73-b8a1-66429f69f2b0n@googlegroups.com>
<1159ca4a-6452-4317-8367-d7ff155799d4n@googlegroups.com> <eabc9b91-3637-4ea8-b80d-25ae8d872a92n@googlegroups.com>
<bb08354f-1bd6-47c8-a630-2839f0ca3625n@googlegroups.com> <f1a5dfc3-ffdc-4fad-9737-461c80962075n@googlegroups.com>
<4310ea50-2f05-42f0-be3f-cb48e3175eb2n@googlegroups.com> <721ef121-7390-4772-be6a-986665480964n@googlegroups.com>
<06e0b912-a764-42c1-ad50-eb2c410d2dcen@googlegroups.com> <1fe9fe24-ef19-486d-b3c0-7743e6dab69bn@googlegroups.com>
<9d419dee-473d-493a-b099-044a2c4b783dn@googlegroups.com> <6b5eccf4-e9ed-4654-8ed4-1a00c5ff5f5en@googlegroups.com>
<3bd05f4a-3b2e-49b3-b7c7-7b05f2afae13n@googlegroups.com> <f81cc95e-7491-4704-8484-0399990dbddbn@googlegroups.com>
<f0ea98e1-fb57-4fc7-9b2e-fd74b9aaa04an@googlegroups.com> <b9453197-ef5a-4fe3-8cb0-76c3af5e9ae6n@googlegroups.com>
<d1436fb7-195b-418b-91bc-9305a3e710a7n@googlegroups.com> <95c178d8-c38f-4999-a5d5-0616d25392afn@googlegroups.com>
<d13957b7-104d-4a2d-b0e9-a7a03ec66b3cn@googlegroups.com> <24e77d9c-cad9-49f7-ac97-82db28d9692en@googlegroups.com>
<63debfaa-4e79-418e-9577-c3d4183a6f0bn@googlegroups.com> <58e48110-a7e2-4776-b1ed-978e6d240e2bn@googlegroups.com>
<97d27255-d796-4b1c-a30a-44226dba0c37n@googlegroups.com> <7d9f82cc-e322-468d-8deb-bcdbc8e11e3cn@googlegroups.com>
<f3bb9919-58cd-4915-8f3b-583968e299c5n@googlegroups.com> <6ece56a0-5d42-43d2-bf14-d3af90c8ba4dn@googlegroups.com>
<bcc065b7-9396-4fbf-a33a-1974cca890e3n@googlegroups.com> <532fa42a-d34d-4f4d-9e85-ed1556ff9d16n@googlegroups.com>
<87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <527cbd43-e474-4449-8dcc-dfa996d63c2fn@googlegroups.com>
Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 31 May 2022 20:19:08 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

X-Received: by 2002:a05:622a:13:b0:301:6d0d:c731 with SMTP id x19-20020a05622a001300b003016d0dc731mr13123206qtw.43.1654028790887;
Tue, 31 May 2022 13:26:30 -0700 (PDT)
X-Received: by 2002:a25:5b08:0:b0:65b:9a0e:6212 with SMTP id
p8-20020a255b08000000b0065b9a0e6212mr3625725ybb.212.1654028790459; Tue, 31
May 2022 13:26:30 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 13:26:30 -0700 (PDT)
In-Reply-To: <f3ec52aa-b308-928e-84fe-70fa2e298ace@att.net>
Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7727:573c:1f2:a917:58fc:dc77;
posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b
NNTP-Posting-Host: 2003:e4:7727:573c:1f2:a917:58fc:dc77
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<725c42dd-3000-41bc-bdeb-b114c3d3de9cn@googlegroups.com> <94252f9a-0ced-1224-3b51-f79c9454dd05@att.net>
<12196cf5-a7ec-4297-9d1c-4e182a9ed9fbn@googlegroups.com> <e68a7682-8c0a-32eb-0f4a-2cff19e0c76f@att.net>
<0eedcd9e-f120-4151-a960-036acb36fafen@googlegroups.com> <37a4026a-46e1-cfbc-cdf6-2885d39eb4f4@att.net>
<19bcfc7c-5e49-4143-98cb-6253a3fb2412n@googlegroups.com> <1fbd8314-78bf-8437-cfb5-ddf782fcd7d5@att.net>
<f328880c-52f3-46f2-8ff5-1e2e2ff86592n@googlegroups.com> <c1e9d912-fc3f-0d1d-3e32-1f2a55d4463c@att.net>
<9e2f663c-7c97-4408-bab1-05a778f90901n@googlegroups.com> <0cadf616-d229-7a8a-7c89-4e4b7349703f@att.net>
<bd71bb8c-a9cc-4deb-a7ef-4faf950faecfn@googlegroups.com> <eba05ea8-58c8-2b48-969c-9989d8e0c457@att.net>
<fb3831a2-7ee8-4022-b4d3-332ba7184673n@googlegroups.com> <b8469877-db01-4387-23c7-99e45eaea0e4@att.net>
<d9f1fe53-859d-4afb-b1d7-773ec13ccfa3n@googlegroups.com> <f3ec52aa-b308-928e-84fe-70fa2e298ace@att.net>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <c70dc95c-69dc-4dfd-8e1a-98fcfcaf9972n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 31 May 2022 20:26:30 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 3126

Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 31 May 2022 16:59:32 -0400
Organization: A noiseless patient Spider
Lines: 45
Message-ID: <913c9abf-22c3-0fd1-a492-0afa7ea81840@att.net>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<12196cf5-a7ec-4297-9d1c-4e182a9ed9fbn@googlegroups.com>
<e68a7682-8c0a-32eb-0f4a-2cff19e0c76f@att.net>
<0eedcd9e-f120-4151-a960-036acb36fafen@googlegroups.com>
<37a4026a-46e1-cfbc-cdf6-2885d39eb4f4@att.net>
<19bcfc7c-5e49-4143-98cb-6253a3fb2412n@googlegroups.com>
<1fbd8314-78bf-8437-cfb5-ddf782fcd7d5@att.net>
<f328880c-52f3-46f2-8ff5-1e2e2ff86592n@googlegroups.com>
<c1e9d912-fc3f-0d1d-3e32-1f2a55d4463c@att.net>
<9e2f663c-7c97-4408-bab1-05a778f90901n@googlegroups.com>
<0cadf616-d229-7a8a-7c89-4e4b7349703f@att.net>
<bd71bb8c-a9cc-4deb-a7ef-4faf950faecfn@googlegroups.com>
<eba05ea8-58c8-2b48-969c-9989d8e0c457@att.net>
<fb3831a2-7ee8-4022-b4d3-332ba7184673n@googlegroups.com>
<b8469877-db01-4387-23c7-99e45eaea0e4@att.net>
<d9f1fe53-859d-4afb-b1d7-773ec13ccfa3n@googlegroups.com>
<f3ec52aa-b308-928e-84fe-70fa2e298ace@att.net>
<c70dc95c-69dc-4dfd-8e1a-98fcfcaf9972n@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: reader02.eternal-september.org; posting-host="25b5a0290612ac3ec1f3b9bba5aa0802";
logging-data="3472"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19O8VDlwC+lsLBsKAvvjrIY3exMoiBcpao="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Cancel-Lock: sha1:g0zI0QREHmU0qeck7eTMixMF0rw=
In-Reply-To: <c70dc95c-69dc-4dfd-8e1a-98fcfcaf9972n@googlegroups.com>
Content-Language: en-US

X-Received: by 2002:a05:622a:64c:b0:2f9:a4c:b4f0 with SMTP id a12-20020a05622a064c00b002f90a4cb4f0mr50174675qtb.380.1654034090479;
Tue, 31 May 2022 14:54:50 -0700 (PDT)
X-Received: by 2002:a25:c201:0:b0:654:36f9:f76b with SMTP id
s1-20020a25c201000000b0065436f9f76bmr35446370ybf.339.1654034090193; Tue, 31
May 2022 14:54:50 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Tue, 31 May 2022 14:54:49 -0700 (PDT)
In-Reply-To: <527cbd43-e474-4449-8dcc-dfa996d63c2fn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=159.2.170.162; posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I
NNTP-Posting-Host: 159.2.170.162
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
<af0e6d1b-b93a-48b0-b6db-501f95087564n@googlegroups.com> <16a4fb02-4ce0-4b85-94f2-1da4eec4bc27n@googlegroups.com>
<eb9e17d7-40bb-4d67-9201-9faa19302c16n@googlegroups.com> <34375b13-2fab-4927-b903-692b0798dbefn@googlegroups.com>
<0861ac88-84d8-48f0-831e-d5efe07c3ee2n@googlegroups.com> <f7ee355b-07d0-4b2a-82fb-c6477aab1232n@googlegroups.com>
<d6dd91c6-5756-4508-80a5-fd713d70351an@googlegroups.com> <d08db3bd-1624-4dd2-86b0-e5c336f2d907n@googlegroups.com>
<fc6a3664-b6cf-4cdd-9bc9-f6706575f51dn@googlegroups.com> <01d8dbb8-c6b6-4eac-a826-9d9217251a9fn@googlegroups.com>
<23ef8249-b7df-433f-974b-31b97f4db7bbn@googlegroups.com> <2314f69a-0262-4c26-9fc3-e708a567e196n@googlegroups.com>
<c442a802-2246-42cd-8f5e-2b4e40b631f0n@googlegroups.com> <9612dc60-7676-4417-9cd1-220e6d065132n@googlegroups.com>
<a6e7fe44-87f6-478d-a3e5-435f1d0461bcn@googlegroups.com> <be871dfb-288a-4b43-a8b1-2fa052b8edc1n@googlegroups.com>
<e610493d-5a8e-4055-a95c-0ad8568da48an@googlegroups.com> <c79a4186-dc4e-4cac-865e-6e7d45d586b1n@googlegroups.com>
<60955268-b979-4f46-89b3-97b373faa806n@googlegroups.com> <d6b21676-3dab-4097-87e4-8510cc520efen@googlegroups.com>
<4c053909-87ce-4285-991b-368c8b212b2dn@googlegroups.com> <5f31dc55-0a92-475d-8b13-4f6a871654bfn@googlegroups.com>
<a6b0f80c-9559-4508-9760-84313d7ecf10n@googlegroups.com> <feb0aa7f-69ef-4698-b25c-935aeb96d67bn@googlegroups.com>
<ef4a445e-de91-4271-8e2e-b2d3aeb50d81n@googlegroups.com> <4837804e-ee17-4804-80b4-0c17f00a4d7an@googlegroups.com>
<ef491fdd-6e20-4fea-8f84-497046dac5b3n@googlegroups.com> <01db1bca-c6fc-4ba8-be75-37ce679b070dn@googlegroups.com>
<fcd32c40-18c2-457d-8f71-e2d378bf3288n@googlegroups.com> <756a88cf-a3e6-4ad9-93dc-627eef357e8dn@googlegroups.com>
<9756fced-2bdf-4272-8801-b2654392c1f1n@googlegroups.com> <cb59dff5-96b9-4dd9-97d6-37edafce6ce1n@googlegroups.com>
<b5d8aee2-192b-4d12-ac63-a8ff320e4863n@googlegroups.com> <c46a3018-a3e1-4602-a4a9-7944a734e2b9n@googlegroups.com>
<79bf5344-9cad-4a6b-b14d-355828f5fa36n@googlegroups.com> <5482bad8-4c32-4ac4-bf4f-968e96c5159en@googlegroups.com>
<55d5c2fd-8c1d-4fd9-891f-2948b0a6081en@googlegroups.com> <137ba311-30ec-43bf-a78e-f46c1e412464n@googlegroups.com>
<435a423f-5c70-4349-ac0e-cb91b10c89a1n@googlegroups.com> <c8e83a2d-ca6f-4580-a232-38344b5f3141n@googlegroups.com>
<cbc1a821-f7d1-4b92-83c6-c01111f6ba4fn@googlegroups.com> <1260682a-990d-40da-aec4-ee194a95b07cn@googlegroups.com>
<60052711-3f3e-423e-bf83-9c2628aa7401n@googlegroups.com> <ac680fc3-78ef-476b-9e7a-513c848b4c94n@googlegroups.com>
<6a4c7b09-6de2-412e-8bf9-e17c1e6bf990n@googlegroups.com> <173c6ac0-13c7-42d5-8bf3-64e8f0fc0556n@googlegroups.com>
<447d479e-8fd1-4fb0-861b-da083da557den@googlegroups.com> <667344fe-c5e4-46ed-a129-2c41a380cfbbn@googlegroups.com>
<94ef4c02-445f-4258-856b-99453396509fn@googlegroups.com> <89eb596a-6480-44be-ab59-6d9be7a1ac03n@googlegroups.com>
<30096113-38b6-459b-96ce-17f8c87df610n@googlegroups.com> <a41e936d-7f27-4cf5-894c-43adb12278edn@googlegroups.com>
<3c503871-597b-4d9e-8184-68259c58b2a8n@googlegroups.com> <6fd21408-ab3c-4714-8213-48c455839334n@googlegroups.com>
<e145a374-18cc-4671-8325-2f8e50fce523n@googlegroups.com> <0a1a58b1-6d1d-4f01-ac00-0f2d6be020abn@googlegroups.com>
<8db140e2-bec7-479f-913a-b63c7b702f7bn@googlegroups.com> <bd266bcf-6197-4ec3-9784-098ec2605d6fn@googlegroups.com>
<7733ec3e-56f2-4b5c-964d-fb9e130c0bccn@googlegroups.com> <1611b520-8d07-474b-ad6f-a0e4d18eb996n@googlegroups.com>
<5f0a82ca-d1a8-44ee-9603-44787c624683n@googlegroups.com> <6ca7d142-8c2c-4e25-aca9-53ea0cd319c2n@googlegroups.com>
<5112d49b-03fe-4e53-bb4c-332d3ce272e7n@googlegroups.com> <57fa08b3-751e-4680-be7e-2632f96d0f48n@googlegroups.com>
<f1685be4-7ba3-43c2-b48c-d9c480d205cbn@googlegroups.com> <9614a5a5-94c1-4639-9334-85f5091164dfn@googlegroups.com>
<62fd07f5-3b15-42ab-804f-2817db3baa70n@googlegroups.com> <98bda7c3-63a8-459d-aa4e-d442ccd44427n@googlegroups.com>
<8bfc098d-8fad-4ee8-82a6-5dc18d912c89n@googlegroups.com> <c37630ee-12e0-4421-b8b0-55d3c3f04496n@googlegroups.com>
<23e46415-1bf1-4399-88fa-3e3ebe47efcan@googlegroups.com> <d768f058-126d-434a-9551-005344a6cf36n@googlegroups.com>
<2eed664f-4083-4c87-89e2-7a71219d7ffen@googlegroups.com> <b5470a4c-1fde-4b73-b8a1-66429f69f2b0n@googlegroups.com>
<1159ca4a-6452-4317-8367-d7ff155799d4n@googlegroups.com> <eabc9b91-3637-4ea8-b80d-25ae8d872a92n@googlegroups.com>
<bb08354f-1bd6-47c8-a630-2839f0ca3625n@googlegroups.com> <f1a5dfc3-ffdc-4fad-9737-461c80962075n@googlegroups.com>
<4310ea50-2f05-42f0-be3f-cb48e3175eb2n@googlegroups.com> <721ef121-7390-4772-be6a-986665480964n@googlegroups.com>
<06e0b912-a764-42c1-ad50-eb2c410d2dcen@googlegroups.com> <1fe9fe24-ef19-486d-b3c0-7743e6dab69bn@googlegroups.com>
<9d419dee-473d-493a-b099-044a2c4b783dn@googlegroups.com> <6b5eccf4-e9ed-4654-8ed4-1a00c5ff5f5en@googlegroups.com>
<3bd05f4a-3b2e-49b3-b7c7-7b05f2afae13n@googlegroups.com> <f81cc95e-7491-4704-8484-0399990dbddbn@googlegroups.com>
<f0ea98e1-fb57-4fc7-9b2e-fd74b9aaa04an@googlegroups.com> <b9453197-ef5a-4fe3-8cb0-76c3af5e9ae6n@googlegroups.com>
<d1436fb7-195b-418b-91bc-9305a3e710a7n@googlegroups.com> <95c178d8-c38f-4999-a5d5-0616d25392afn@googlegroups.com>
<d13957b7-104d-4a2d-b0e9-a7a03ec66b3cn@googlegroups.com> <24e77d9c-cad9-49f7-ac97-82db28d9692en@googlegroups.com>
<63debfaa-4e79-418e-9577-c3d4183a6f0bn@googlegroups.com> <58e48110-a7e2-4776-b1ed-978e6d240e2bn@googlegroups.com>
<97d27255-d796-4b1c-a30a-44226dba0c37n@googlegroups.com> <7d9f82cc-e322-468d-8deb-bcdbc8e11e3cn@googlegroups.com>
<f3bb9919-58cd-4915-8f3b-583968e299c5n@googlegroups.com> <6ece56a0-5d42-43d2-bf14-d3af90c8ba4dn@googlegroups.com>
<bcc065b7-9396-4fbf-a33a-1974cca890e3n@googlegroups.com> <532fa42a-d34d-4f4d-9e85-ed1556ff9d16n@googlegroups.com>
<87605f9f-dc32-47ce-9a18-c06f4d0c6456n@googlegroups.com> <527cbd43-e474-4449-8dcc-dfa996d63c2fn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <b93be345-7443-406c-94d3-9e1004a9cd25n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Tue, 31 May 2022 21:54:50 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 8041