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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: Tue, 8 Oct 2024 09:45:38 -0400
Organization: i2pn2 (i2pn.org)
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On 10/8/24 4:48 AM, WM wrote:
> On 07.10.2024 14:11, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
> 
>>> You have not understood that all unit fractions are separate points on
>>> the positive axis.
>>
>> I understand that full well.
> 
> Then you understand that every point, if existing, is independent of the 
> others. All unit fractions are points with uncounably many points 
> between each pair. Hence all must be visible including the point next to 
> zero, but they are not.

Just because the concept of points being next to point is just nonsense 
and contradictory.

>>> A shrinking infinite set which remains infinite has an infinite core.
>>
>> Again, no.  There is no such thing as a "core", here.  Each of these sets
>> has an infinitude of elements.  No element is in all of these sets.
> 
> Try to think better. A function of sets which are losing some elements 
> but remain infinite, have the same infinite core. That argument is 
> absolutely definite, a logical necessity. If you cannot understand it, 
> then it is useless to continue this discussion.
> 

Nope, YOUR logic is deficient, and since you insist on holding to it, 
you are getting nowhere.

> Regards, WM
>