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

It happens that WM formulated :

On 06.01.2025 22:51, FromTheRafters wrote:

WM presented the following explanation :

On 06.01.2025 19:23, FromTheRafters wrote:

WM pretended :
>

0 is a cardinal but not an ordinal.

>
Wrong.

>
Who is the zeroest clown?

 Okay, maybe not with "your" definition of the ordinal numbers.

>
Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc [Wikipedia]

From the same source:
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https://en.wikipedia.org/wiki/Ordinal_number#Von_Neumann_definition_of_ordinals
First several von Neumann ordinals
0 = {} = ∅
1 = {0} = {∅}
2 = {0,1} = {∅,{∅}}
3 = {0,1,2} = {∅,{∅},{∅,{∅}}}
4 = {0,1,2,3} = {∅,{∅},{∅,{∅}},{∅,{∅},{∅,{∅}}}}
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Notice they start at zero (emptyset)
https://en.wikipedia.org/wiki/Ordinal_numeral
Says:
For the mathematical concept, see Ordinal number.