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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Mon, 7 Oct 2024 11:08:33 +0200
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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.

> Bijection is not about completeness, countability is.

Bijective means injective and surjective.

> 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.

> 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.

Regards, WM