Re: Replacement of Cardinality

Am Fri, 02 Aug 2024 11:38:33 +0000 schrieb WM:

Le 01/08/2024 à 18:04, joes a écrit :

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

 

Every eps interval around 0 contains unit fractions which cannot be
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.

Well, there's no epsilon that separates all positive numbers from zero.
But every fraction has an epsilon that is smaller.

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.

And no sequence of omega - k.

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.

Following the WHOLE of the natural numbers. The successor of a natural
is also one.

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

ω

Ah, a natural 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.