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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Mon, 6 Jan 2025 18:57:49 +0100
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On 06.01.2025 13:28, Richard Damon wrote:
> On 1/5/25 2:47 PM, WM wrote:

>> You said that I never used all FISONs. But I do. All are insufficient.
> 
> No, you DON'T use all. Because ALL has an infinite number of members,

All are less than |ℕ|/10000.

> and you need to process them one by one,

I do not process them but use my theorem: Every union of FISONs which 
stay below a certain threshold stays below that threshold.
>>> but your claim doesn't match your conclusion, as the union of *ALL* 
>>> the FISIONs will reach the size of the Natural Numbers, even though 
>>> no finite subset reaches a measurable percentage of it.
>>>
>> How do they do it? Do one or more FISONs grow during the union 
>> process? (One would be sufficient.)
> 
> Nope, they are just infinite in number.

The set of all rationals between 0 and 1 is also infinite in number. 
That is not an argument for their union to reach |ℕ|.

Regards, WM