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

Am Fri, 10 Jan 2025 17:19:44 +0100 schrieb WM:

On 10.01.2025 13:41, Richard Damon wrote:

On 1/9/25 7:37 AM, WM wrote:

 

As I said, cardinality cannot describe this difference of one element.

Because the property that "cardinality" describes doesn't have that
difference.

So it is. Cardinality cannot describe the difference of one element, not
even of infinitely many.

Depends. The complement of a starting segment of N (wrt N) is infinite;
the primes are infinite although also a subset.

Infinite is simply infinite, no matter what the real size is.

There is no "real size", there is only the set. Your expectations
about cardinality do not match it.

You need not understand that. But the claim that different sets like ℕ
and ℚ are of same size shows that you have been stultified by set
theory.

They have the same cardinality, defined as being bijective.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.