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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Mon, 7 Oct 2024 15:18:30 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 07 Oct 2024 11:08:33 +0200 schrieb WM:
> On 07.10.2024 10:05, joes wrote:
>> Am Mon, 07 Oct 2024 09:41:23 +0200 schrieb WM:
>>> On 06.10.2024 17:48, Alan Mackenzie wrote:
>>> even an unbounded sequence does not get longer when shifted by one
>>> step.
>> Nor does it get shorter, it stays infinite.
> It keeps all its elements but not more.
„More” being a different kind of infinity, namely at least uncountable.
All ω+k are equally infinite.

>> Bijection is not about completeness, countability is.
> Bijective means injective and surjective.
Exactly, which is the case for every finite subset.

>> Of course stopping after a finite number, which potential infinity
>> seems to mean, is not „complete” in that sense. Hilbert’s Hotel is
>> actually infinite, it already holds infinite guests.
> Name them by all the natural numbers. Then no further guest can appear.
It can, if I begin numbering with 2. The cardinality of N\{1} can’t be
finite.

>> All of them can at once move to the next room,
> All rooms are enumerated by all the natural numbers. Hence there is no
> chance to move. Only in potential infinity there is.
Huh? They are all fixed, we can move them „rigidly”.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.