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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 5 Jan 2025 13:04:59 +0100
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On 05.01.2025 12:28, Alan Mackenzie wrote:
> WM <wolfgang.mueckenheim@tha.de> wrote:

> The set of these prime gaps is infinite, without qualification.  Euclid
> could have told you that.

Euclid did not believe in actual infinity. The prime gaps have no upper 
limit.
> 
>> Finally, the most familiar example is this: The (magnitudes of) natural
>> numbers are potentially infinite because, although there is no upper
>> bound, there is no infinite (magnitude of a) natural number.
> 
> There are no "actual" and "potential" infinity in mathematics.

It has been exorcized by those matheologians who were afraid of the 
problems introduced to matheology by these precise definitions.

> The
> notions are fully unneeded, and add nothing to any mathematical proof.
> There is finite and infinite, and that's it.
> 
> When I did my maths degree, several decades ago, "potential infinity" and
> "actual infinity" didn't get a look in.  They weren't mentioned a single
> time.

That has opened the abyss of nonsense to engulf mathematics with such 
silly results as: A union of FISONs which stay below a certain threshold 
can surpass that threshold.
> 
> The only people who talk about "potential" and "actual" infinity are
> non-mathematicians who lack understanding, and pioneer mathematicians
> early on in the development of set theory who were still grasping after
> precise notions.

All mathematicians whom you have disqualified above are genuin 
mathematicians.

What you