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

On 12/2/2024 3:53 AM, FromTheRafters wrote:

Chris M. Thomasson brought next idea :

On 11/30/2024 3:12 AM, WM wrote:

On 30.11.2024 11:57, FromTheRafters wrote:

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).

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Endsegments are defined as infinite,

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

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As what is left after not considering a finite initial segment in your new set and considering only the tail of the sequence.

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Not quite but roughly. The precise definitions are:
Finite initial segment F(n) = {1, 2, 3, ..., n}.

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Finite? Huh? The natural numbers don't stop at n! WTF!!!!  Lay off the drugs.

 That ordered set has a first element namely '1' and a last element, namely 'n' so yes, it is finite.

I was thinking that WM thinks that n is a magical largest natural number. { 1, 2, 3, ... } = the_set_of_all_natural_numbers
Not showing an end point for it ala n. I got confused.

 

Endsegment E(n) = {n, n+1, n+2, ...}

 This is his definition of endsegment, which as almost anyone can see, has no last element, so yes it is infinite. He says 'infinite endsegment' as if there were a choice, only to add confusion.