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

Am Thu, 09 Jan 2025 17:51:43 +0100 schrieb WM:

On 09.01.2025 13:18, Richard Damon wrote:

On 1/9/25 6:39 AM, WM wrote:

On 09.01.2025 01:07, joes wrote:

Am Wed, 08 Jan 2025 22:57:52 +0100 schrieb WM:

>

The rule is for n there is n+1. But the successor is not created but
does exist. How far do successors reach? Why do they not reach to
ω-1?
Where do they cease before?

They don't cease. They simply aren't in the same league, if you will.

Cantor will. Every set of numbers of the first and second number class
has a smallest element. Hence they all are on the ordinal line.

Which doesn't prove your claim,

It proves that the numbers of the first and second number class form a
linear system.

Is the second class all infinite(!) ordinals >= omega but less than
omega*2, or until epsilon_0? Either way, all ordinals have an order,
but omega still has no predecessor (and omega*2 doesn't, and all
omega*k for k e N, and omega^j+omega*k...).

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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.