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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?
Date: Sat, 7 Sep 2024 15:31:09 +0200
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On 07.09.2024 14:58, Richard Damon wrote:
> On 9/7/24 8:55 AM, WM wrote:
>> On 07.09.2024 04:01, Richard Damon wrote:

>>> But it CAN'T for the values of x that are finite, as for ANY finite 
>>> number, there is an infinite number of unit factions below it, so it 
>>> can't ever have a finite value for any finite x.
>>
>> This idea must be dropped.

> Then the idea that NUF(x) "increases by one" at the values of "unit 
> fractions" must be dropped.
> 
> Sorry, you can't have one without the other.

Then logic breaks down because identical elements differ.
The unit fractions are identical because they sit at the same x, but 
they differ because they are ℵo different unit fractions.

Logic or the successor axiom? Without the former the latter would be 
useless.

Regards, WM