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Successor set
Set
context | $X$ |
definiendum | $ S(X) \equiv X \cup \{X\} $ |
Discussion
Theorems
$ X\in S(X) $ |
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$ (S(X)=S(Y))\Rightarrow (X=Y) $ |
$ (Y\in S(X))\Leftrightarrow (Y=X\lor Y=\{X\}) $ |
$ X\neq S(X) $ |
Reference
Wikipedia: Successor ordinal
ProofWiki: Successor set