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

WM was thinking very hard :

On 07.01.2025 15:05, FromTheRafters wrote:

WM wrote :

On 07.01.2025 10:51, FromTheRafters wrote:
>

First several von Neumann ordinals

>
v. Neumann was bright but not bright enough.
Why should we use the nomenclature of his disproven theory?

>
Disproven?
>

0     =     {}     =     ∅
1     =     {0}     =     {∅}
2     =     {0,1}     =     {∅,{∅}}
3     =     {0,1,2}     =     {∅,{∅},{∅,{∅}}}
4     =     {0,1,2,3}     =     {∅,{∅},{∅,{∅}},{∅,{∅},{∅,{∅}}}}
=====================================
>
Notice they start at zero (emptyset)

>
It would be more important to reach the full set.

>
It does, in the infinite union.

>
It does not because the infinite union cannot be larger than every unioned FISON.

 Just because you saya so?

 

Every unioned FISON is smaller than any definable fraction of the full set ℕ.

 So what?