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

Am Sun, 12 Jan 2025 12:19:15 +0100 schrieb WM:

On 11.01.2025 14:58, joes wrote:

Am Sat, 11 Jan 2025 12:44:59 +0100 schrieb WM:

 

∀n ∈ ℕ: |{1, 2, 3, ..., 2n}|/|{2, 4, 6, ..., 2n}| = 2.

Your claim does not hold for the sets.

That may be if sets are considered as more than their elements. My
claims hold for all their elements.

I am talking about the sets N and E. They are infinite, so you are
saying nothing about them, only about finite subsets.

My claim holds for all natnumbers only.

And not for infinity.

No numbers are "created"

There is no "after" an infinity.

Wrong. 1 is after an infinity of (unit) fractions.

Turn it around and there is nothing before.

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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.