Re: Replacement of Cardinality

Le 01/08/2024 à 18:04, joes a écrit :

Am Thu, 01 Aug 2024 12:27:27 +0000 schrieb WM:

separated from 0 by any eps. Therefore your claim is wrong.

No. There is ALWAYS an epsilon.

Failing to separate almost all unit fractions.
Don't claim the contrary. Define (separate by an eps from 0) all unit fractions. Fail.

>

What is the reason for the gap before omega? How large is it? Are these
questions a blasphemy?

A "gap" implies some sort of space that is not filled. There is no such
space (it would be filled with infinitely many natural numbers).

Hence there is only the sequence of natnumbers.

We just condense the whole of N into one concept and call that omega,

That is nonsense. ω is the first number following upon all natural numbers.

or add it on the next level of infinity.

Yes.

Your questions are only a display of your unwillingness to understand
infinity,

They  prove that I understand the real infinity while are (con)fusing potential and actual infinity.

If k did not have a successor, what would k+1 be?

ω
Regards, WM