von Neumann ordinal (original) (raw)

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  Given any ordinal α, the ordinal α+1 (the successor of α) is defined to be α∪{α}.
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  Given a set A of ordinals, ⋃a∈Aa is an ordinal.

If an ordinal is the successor of another ordinal, it is an successor ordinal. If an ordinal is neither 0 nor a successor ordinal then it is a limit ordinal. The first limit ordinal is named ω.

The class of ordinals is denoted 𝐎𝐧.

The von Neumann ordinals have the convenient property that if a<b then a∈b and a⊂b.