Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

WM explained :

On 29.11.2024 22:50, FromTheRafters wrote:

WM wrote on 11/29/2024 :

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The size of the intersection remains infinite as long as all endsegments remain infinite (= as long as only infinite endsegments are considered).

 Endsegments are defined as infinite,

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Endsegments are defined as endsegments. They have been defined by myself many years ago.

As what is left after not considering a finite initial segment in your new set and considering only the tail of the sequence. Almost all elements are considered in the new set, which means all endsegments are infinite.

all of them and each and every one of them.

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The set ℕ = {1, 2, 3, ..., n, n+1, ...} cannot be divided into two consecutive infinite sets. As long as all endsegments are infinite, they contain an infinite subset of ℕ. Therefore all indices are the finite complement of ℕ.
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The intersection is empty.

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Try to understand inclusion monotony. The sequence of endsegments decreases.

In what manner are they decreasing? When you filter out the FISON, the rest, the tail, as a set, stays the same size of aleph_zero.

As long as it has not decreased below ℵo elements, the intersection has not decreased below ℵo elements.

It doesn't decrease in size at all.