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Subject: Re: Question about unbounded infinite sets...
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 14/03/2024 à 20:06, Richard Damon a écrit :
> On 3/14/24 11:38 AM, WM wrote:
>> Le 14/03/2024 à 18:39, Richard Damon a écrit :
>> 
>>> the O goes to where the X was and the X goes to where the O was.
>> 
>> So it is. Never an O goes out of the matrix.
> 
> So you aren't doing it right.
> 
> Why do you say that the O going to the OTHER set never leaves,

It does not leave the matrix.

> and the X 
> that comes from the OTHER set never replaces it?

Every replacement fails to remove an O from the matrix.

>>> All the O's end up at the end of the Row/Column, where they would belong.
>> 
>> Also "the end", i.e., the places where the O can go, belong to the matrix.
> 
> No, they don't,

Where do they go?

> the belong to the SET of Natural Numbers or Unit Fractions.

Of course, but all elements of these sets belong to the matrix.
> 
> The "Natural Number n" is NOT the Rational Number n/1, but they have the 
> same vaule.

Initially every n/1 is indeXed by n.
> 
> The "Unit Fraction 1/n" is NOT the Rational Number 1/n, 

You are wrong. But all that does not remove an O from the matrix.

Regards, WM