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

Am Wed, 11 Dec 2024 15:30:18 +0100 schrieb WM:

On 10.12.2024 23:37, joes wrote:

 >>> You (WM) are considering infinite dark.finite.cardinals,
 >>> which do not exist.
 >> Then analysis is contradicted in set theory.
 >> ∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).

Am Mon, 09 Dec 2024 22:28:41 +0100 schrieb WM:

  >> The limit of the left-hand side is empty, the limit of the
  >> right-hand side is full, i.e. not empty.
  >> I do not tolerate that.
  > What is the RHS limit?

All sets are claimed to be infinite.

Like the quantifier says. But what is the limit?

There is no limit in set theory, contrary to the LHS limit { }.

Why not for the RHS?

All sets are claimed to be infinite. A sequence of infinitely many
numbers cannot lose all numbers "in the limit"

Yes, they can. That’s what the limit means - taken to infinity.

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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.