>>780
(引用開始)
ここ、下記の”graphical "matchstick" representation”が、分かり易い
"matchstick"は、21世紀では死語かも。後述のマッチwikipediaご参照
https://en.wikipedia.org/wiki/Ordinal_number
Ordinal number
https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Ordinal_ww.svg/384px-Ordinal_ww.svg.png
A graphical "matchstick" representation of the ordinal ω2. Each stick corresponds to an ordinal of the form ω・m+n where m and n are natural numbers.

There are infinite ordinals as well: the smallest infinite ordinal is ω, which is the order type of the natural numbers (finite ordinals) and that can even be identified with the set of natural numbers. Indeed, the set of natural numbers is well-ordered?as is any set of ordinals?and since it is downward closed, it can be identified with the ordinal associated with it (which is exactly how ω is defined).
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.)
(引用終り)

"matchstick"は、現在だと、”つまようじ”（下記）くらいか。まあ棒だと思ってください
図”graphical "matchstick" representation”で、一番左が、0（ゼロ）です
そして、0から右へ行くと、棒が小さくなる。極限順序数ωで、棒の長さは0になる

ちょうど>>750の一対一対応
無限上昇列：1<　2<　3<・・<　n<・・
　　　　　　　　　↓↑
無限下降列：1> 1/2> 1/3>・・> 1/n>・・
を図示したかっこうですね

そして、次にω＋1が、また始まるのです。

つづく