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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: Fri, 1 Nov 2024 18:33:34 +0100
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On 01.11.2024 16:04, Jim Burns wrote:

> Here,
> you say: the smallest exists.
> That does not pop the smallest into existence.

I say: All exist. That implies the smallest.
> 
> It contracts our discourse to
> lines which have a smallest.

Yes.

The other alternative would consist of variable sets.
>> Why?
>> It is a point on the real line,
>> well separated from its neighbour.
> 
> You can contract our discourse to
> real lines with smallest points,
> but they will also be
> real lines without smallest points,

That happens when Cantor's actual infinity is treated like potential 
infinity. Best example: Hilberts hotel.

Regards, WM