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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 20 Oct 2024 17:54:56 -0400
Organization: i2pn2 (i2pn.org)
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On 10/20/24 3:39 PM, WM wrote:
> On 20.10.2024 21:30, Richard Damon wrote:
> 
>> No, the alternative is that infinite sets work like infinite sets 
>> without an end, and that this means that some of the properties of 
>> finite sets don't hold for infinite sets.
>>
> When the density is reduced and the number remains the same, then the 
> size is increased. Not accepting this means violating mathematics.
> 
> Regards, WM
> 

The concept of "density" as you are trying to use it just isn't 
applicable when you try to look at a finite subset of the infinite sets.


The real problem is you keep on trying to use "finite" logic on infinite 
set/numbers, and it just can't handle them, because some of the rules 
are different.

All you have done is proved that your logic just can't handle the 
infinite, not that the infinite doesn't exist.