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

Am Fri, 10 Jan 2025 18:21:43 +0100 schrieb WM:

On 10.01.2025 18:01, joes wrote:

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:

>

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

There is no "real size", there is only the set.

There is real size. The natural numbers have twice the size of the even
numbers.

No, the even numbers are twice the naturals.

Your expectations about cardinality do not match it.

I have no expectations about cardinality. I know that for every finite
initial segment the even numbers are about half of the natural numbers.
This does not change anywhere. It is true up to every natural number.
More are not available.

You wrongly expect this to hold in the infinite.

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.

Already the bijection between even and natural numbers has been
disproved above.

You are mistaken. Clearly |{1*2, 2*2, 3*2, ...}| = |N|

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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.