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

On 07.01.2025 13:35, Richard Damon wrote:

On 1/7/25 5:20 AM, WM wrote:

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.

 No, ZF doesn't have as an axiom that the set of Natural Numbers exist.

AoI: There exists an infinite set S.

All FISONs stay below the threshold |ℕ|/100, or in other words, multiplication of any FISON by 100 is insufficient to cover |ℕ|.
>

 So? The union of an infinite set of them can have properites different that any set that is a union of only a finite number of them. That is a nature of infinity.

It is the nature of fools to believe every nonsense.

 

Every union of FISONs {1, 2, 3, ..., n} which stay below this threshold stays below this threshold too.

 But not the union of *EVERY* FISON, the FULL INFINITE set of them.

All are below 1 %.

SOething your "logic" can't handle,

Luckily.
Regards, WM