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

On 07.01.2025 14:49, FromTheRafters wrote:

WM was thinking very hard :

On 07.01.2025 02:36, Ross Finlayson wrote:

On 01/06/2025 02:43 PM, Jim Burns wrote:

>

It would be great if you (WM) did NOT
find lemma 1 weird,
but it is what it is.

>
It is not weird. But your conclusions are weird.
>

The inductive set being covered by
initial segments is an _axiom_ of ZF.

>
And the existence of the set ℕ is also an axiom of ZF.

 Which axiom?

>
The axiom of infinite set. The elements of the infinite set have been designed after Dedekind as Zermelo, the creator of the axiom himself confesses. Its elements can be called cardinal numbers.