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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)
Date: Wed, 11 Dec 2024 20:57:29 +0100
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On 11.12.2024 20:27, Jim Burns wrote:

> 
> ⋂{E(i):i} = {}.

Of course. But all intersections with finite contents are invisible.

> Therefore,
> one.element.emptier ℕ\{0}
> is not.smaller.than ℕ

It is a smaller set. Cardinalities are not useful.
> 
> That is the reason that
> the end.segments of ℕ
> stay the same larger.than.any.finite size
> as they lose each element of ℕ.

The intersection of all is empty. The sequence of intersections cannot 
lose more than one element per term. The terms immediately before the 
empty intersection are finite.

Regards, WM