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

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. Therefore ZF is incompatible with mathematics.
|ℕ| is a fixed quantity larger than every n, by any factor, for instance by the factor 100.
All FISONs stay below the threshold |ℕ|/100, or in other words, multiplication of any FISON by 100 is insufficient to cover |ℕ|.
Every union of FISONs {1, 2, 3, ..., n} which stay below this threshold stays below this threshold too.
Regards, WM