>>484
>あなたの云うスタンダードとは何でしょう？

下記”Ordinal number”の通りです
（”Ordinals were introduced by Georg Cantor in 1883[3] in order to accommodate infinite sequences and classify derived sets”）

>ωを第何項目に追加したんですか？

その”第何項目”という問いは、自然数の中だよね
で、下記の通り、”the first infinite ordinal, ω”は、”After all natural numbers comes ”なので、全ての自然数の外で、自然数の外に追加しました

分からなければ、下記の”Ordinal number”のリンクを開いて、全文を百回音読してください

https://en.wikipedia.org/wiki/Ordinal_number#Von_Neumann_definition_of_ordinals
Ordinal number
(抜粋)
Ordinals were introduced by Georg Cantor in 1883[3] in order to accommodate infinite sequences and classify derived sets, which he had previously introduced in 1872?while studying the uniqueness of trigonometric series.[4]

Ordinals extend the natural numbers
Perhaps a clearer intuition of ordinals can be formed by examining a first few of them: as mentioned above, they start with the natural numbers, 0, 1, 2, 3, 4, 5, … After all natural numbers comes the first infinite ordinal, ω, and after that come ω+1, ω+2, ω+3, and so on. (Exactly what addition means will be defined later on: just consider them as names.)