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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Fri, 31 Jan 2025 05:43:52 -0500
Organization: Peripheral Visions
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References: <vmo1bs$1rnl$1@dont-email.me>   <vmvn1h$25r19$1@dont-email.me> <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <vn2gcf$2ouuo$2@dont-email.me> <d90c478d-6806-4ffe-83be-a5d7674bb5e3@att.net> <b82a0915-400a-4f77-9309-44eef432e9f4@att.net> <vn50eo$3kgi6$2@dont-email.me> <4d349964-211f-42f1-936f-81c22ae54cb5@att.net> <vn7vns$ra97$2@dont-email.me> <e3f89d8c-d214-453a-91f4-9023e744fed2@att.net> <vna72s$1ng1k$2@dont-email.me> <6e0c8ab2-402a-43a5-a348-0c727eae6a2e@att.net> <vnat4s$1s6ha$4@dont-email.me> <e43b1c65-4424-4e0c-9b2e-65e0e463815b@att.net> <vnconr$29v5v$1@dont-email.me> <vncstv$2anvb$1@dont-email.me> <vncuei$2avaj$2@dont-email.me> <vndch7$2dgpn$1@dont-email.me> <vnffg0$2rv3s$4@dont-email.me> <vnfl08$2tga8$1@dont-email.me> <vngj43$31ud4$4@dont-email.me> <vngldd$33j5g$1@dont-email.me> <vngsfu$34ss1$1@dont-email.me> <vngso1$34uah$1@dont-email.me> <vngual$34ss1$4@dont-email.me> <vni73p$3evq7$1@dont-email.me> <vni7ri$3f2gg$1@dont-email.me>
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WM explained :
> On 31.01.2025 11:02, FromTheRafters wrote:
>
>> Ordinals aren't guaranteed to increase.
>
> What ordinal has not a greater successor?
> Ordinals n are well-ordered. The distance from 0 is n - 0 = n.

Starting with omega, they are all countably infinite until you reach 
the uncountably infinite.