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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Tue, 07 Jan 2025 04:51:09 -0500
Organization: Peripheral Visions
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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:
====================================
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} 	= 	{∅,{∅},{∅,{∅}},{∅,{∅},{∅,{∅}}}}
=====================================

Notice they start at zero (emptyset)


https://en.wikipedia.org/wiki/Ordinal_numeral

Says:

For the mathematical concept, see Ordinal number.