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Successor set

Set

context $X$
definiendum $ S(X) \equiv X \cup \{X\} $

Discussion

Theorems

$ X\in S(X) $
$ (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

Parents

Requirements

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