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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: Sun, 22 Dec 2024 12:32:09 +0100
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On 22.12.2024 11:16, Jim Burns wrote:

> What does 'finite' mean?

A set is finite if it contains a visible natural number of elements.
All natural numbers are finite but the realm of dark numbers appears 
like infinity.

> E(n+2) is the set of all finite.cardinals > n+2
> E(n+1)  =  E(n+2)∪{n+2}
> 
> E(n+2)∪{n+2} isn't larger.than E(n+2)

Wrong.

> #E(n+2) isn't any of the finite.cardinals in ℕ

It is an infinite number but even infinite numbers differ like |ℕ| =/= 
|ℕ| + 1. You must not defend Cantor's nonsense by Cantor's nonsense. All 
"countable cardinalities" are the same because only potential infinity 
is utilized.
> 
> E(n+2) isn't any of the sets
> smaller.than fuller.by.one sets.
> 
> E(n+2) is emptier.by.one than E(n+1), but
> E(n+2) isn't smaller.by.one than E(n+1).

Wrong.

The function E(n) decreases from infinity to zero by single steps of 
height 1 like the function NUF(x) increases by single steps of height 1. 
Set theorists must accept magic steps of infinite size or refuse to 
describe these transitions at all.

Regards, WM
> 
>