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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Mon, 02 Dec 2024 10:46:26 -0500
Organization: Peripheral Visions
Lines: 21
Message-ID: <vikkom$3ds36$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>   <vi1vep$2pjuo$1@dont-email.me> <a4ab640d-e482-42b0-bfb8-f3690b935ce1@att.net> <vi41rg$3cj8q$1@dont-email.me> <d124760c-9ff9-479f-b687-482c108adf68@att.net> <vi56or$3j04f$1@dont-email.me> <4a810760-86a1-44bb-a191-28f70e0b361b@att.net> <vi6uc3$3v0dn$4@dont-email.me> <b2d7ee1f-33ab-44b6-ac90-558ac2f768a7@att.net> <vi7tnf$4oqa$1@dont-email.me> <23311c1a-1487-4ee4-a822-cd965bd024a0@att.net> <e9eb6455-ed0e-43f6-9a53-61aa3757d22d@tha.de> <71758f338eb239b7419418f49dfd8177c59d778b@i2pn2.org> <via83s$jk72$2@dont-email.me> <viag8h$lvep$1@dont-email.me> <viaj9q$l91n$1@dont-email.me> <vibvfo$10t7o$1@dont-email.me> <vic6m9$11mrq$4@dont-email.me> <vicbp2$1316h$1@dont-email.me> <vid4ts$1777k$2@dont-email.me> <vidcv3$18pdu$1@dont-email.me> <bdbc0e3d-1db2-4d6a-9f71-368d36d96b40@tha.de> <vier32$1madr$1@dont-email.me> <vierv5$1l1ot$2@dont-email.me> <viiqfd$2qq41$5@dont-email.me> <vik73d$3a9jm$1@dont-email.me> <vikg6c$3c4tu$1@dont-email.me>
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WM wrote :
> On 02.12.2024 12:53, FromTheRafters wrote:
>
>>>> Endsegment E(n) = {n, n+1, n+2, ...}
>> 
>> This is his definition of endsegment, which as almost anyone can see, has 
>> no last element, so yes it is infinite. He says 'infinite endsegment' as if 
>> there were a choice, only to add confusion.
>
> Infinite endsegments contain an infinite set each, infinitely many elements 
> of which are in the intersection. An empty intersection cannot come before an 
> empty endsegment has been produced by losing one element at every step.
>
> E(1), E(2), E(3), ...
> and
> E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
> are identical for every n and in the limit because
> E(1)∩E(2)∩...∩E(n) = E(n).

Non sequitur. That which is true for finite sequences is not 
necessarily true for infinite sequences.