Re: Incompleteness of Cantor's enumeration of the rational numbers

Am Fri, 22 Nov 2024 13:00:52 +0100 schrieb WM:

On 21.11.2024 23:45, joes wrote:

Am Wed, 20 Nov 2024 19:44:39 +0100 schrieb WM:

>

Why? Because only potential infinity is involved. True bijections
prove equinumerosity.

What is a "true" bijection?

A true bijection between two sets proves that both sets have the
same number of elements.

Determined by the sets differing only in a finite number of elements?

Not differing at all.

Ah yes, the sets {-1} u N and {-2} u N  have different sizes.

The number of ℕ \ {1} is 1 less than ℕ.

And what, pray tell, is Aleph_0 - 1 ?

It is "infinitely many" like Aleph_0.

Thanks for agreeing with |N| = |N\{0}|.

Of course. ℵo means nothing but infinitely many.

Good. Then we can consider those sets to have the same number.

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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.