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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: Sun, 19 Jan 2025 05:42:59 -0500
Organization: Peripheral Visions
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WM presented the following explanation :
> On 18.01.2025 12:03, joes wrote:
>> Am Fri, 17 Jan 2025 22:56:13 +0100 schrieb WM:
>
>>> Correct. If infinity is potential. set theory is wrong.
>> And that is why set theory doesn't talk about "potential infinity".
>
> Nevertheless it uses potential infinity.

No, it doesn't.

> All "bijections" yield the same cardinality because only the potentially 
> infinite parts of the sets are  applied.

No, it is because these bijections show that some infinite sets' sizes 
can be shown to be equal even if no completed count exists. A shepherd 
can know that the size of the finite set of sheep which left the corral 
can equal the size of the set of those which returned without actually 
knowing how many sheep there are. Extending this idea to infinite sets 
works just fine despite your idiotic complaints about potential vs. 
actual.