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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?
Date: Sat, 7 Sep 2024 11:02:44 -0400
Organization: i2pn2 (i2pn.org)
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On 9/7/24 9:31 AM, WM wrote:
> 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
> 

Why do you say they are all a x, they are all BELOW x, as there is room 
for them as x is a positive finite value.

You are just showing you don't understand what you are talking about, as 
you like to begin with impossible assumptions. (Because you assume the 
infinite works just like the finite, which it doesn't).


No problem with the successor axiom, you just can't find a "first" to 
take the successor of, as the unit fractions are counted by successor 
from the other end, and there is no "smallest" to start counting from at 
that end.

This just reveals your insanity.