>>380
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（参考）
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 ω^2. Each stick corresponds to an ordinal of the form ω・m+n where m and n are 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.) After all of these come ω・2 (which is ω+ω), ω・2+1, ω・2+2, and so on, then ω・3, and then later on ω・4. Now the set of ordinals formed in this way (the ω・m+n, where m and n are natural numbers) must itself have an ordinal associated with it: and that is ω^2. Further on, there will be ω^3, then ω^4, and so on, and ω^ω, then ω^ω^ω, then later ω^ω^ω^ω, and even later ε0 (epsilon nought) (to give a few examples of relatively small?countable?ordinals). This can be continued indefinitely (as every time one says "and so on" when enumerating ordinals, it defines a larger ordinal). The smallest uncountable ordinal is the set of all countable ordinals, expressed as ω1 or Ω .[4][5][6]

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