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

On 12/1/2024 11:39 PM, Moebius wrote:

Am 02.12.2024 um 00:11 schrieb Chris M. Thomasson:

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

 FINSON(s)
 

Finite initial segment[s]: F(n) = {1, 2, 3, ..., n}   (n e IN)

 You see it's a DEFINITION:
          F(n) = {1, 2, 3, ..., n}   (n e IN) .
 This "means" (implies): F(1) is a FISON (i.e. {1}), F(2) is a FISON (i.e. {1, 2}), F(3) is a FISION (i.e. {1, 2, 3}), and so on (ad infinitum). F(1), F(2), F(3), ... are FISONs.
 

Finite?

 Yeah, finite. For each and eveer n e IN F(n) (i.e. {1, 2, 3, ..., n}) is finite (i.e. a finite set).
 Huh? The natural numbers don't stop at n! WTF!!!
 No one (except possibly Mückenheim) said they did.

Okay. Yeah, I was thinking that WM was using this to denote that n is a largest natural number.

 Hint: There are _infinitely many_ finite initial segments (one for each and every natural number n). :-)

{ { 1 }, { 1, 2 }, { 1, 2, 3 }, ... }
Some FISONS for ya. ;^)