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successor_set [2014/03/27 10:58]
nikolaj
successor_set [2014/12/05 10:51] (current)
nikolaj
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 ==== Set ==== ==== Set ====
 | @#55CCEE: context ​    | @#55CCEE: $X$ | | @#55CCEE: context ​    | @#55CCEE: $X$ |
-| @#FFBB00: definiendum | @#FFBB00: $ S(X\equiv X \cup \{X\} $ |+| @#FFBB00: definiendum | @#FFBB00: $ {\mathrm{succ}}\ ​X \equiv X \cup \{X\} $ |
  
 ==== Discussion ==== ==== Discussion ====
 === Theorems === === Theorems ===
-^ $ X\in S(X$ ^ +^ $ X\in {\mathrm{succ}}\ ​X $ ^ 
-^ $ (S(X)=S(Y))\Rightarrow (X=Y)  $ ^ +^ $ ({\mathrm{succ}}\ ​X={\mathrm{succ}}\ ​Y)\Rightarrow (X=Y)  $ ^ 
-^ $ (Y\in S(X))\Leftrightarrow (Y=X\lor Y=\{X\}) $ ^ +^ $ (Y\in {\mathrm{succ}}\ ​X)\Leftrightarrow (Y=X\lor Y=\{X\}) $ ^ 
-^ $ X\neq S(X$ ^+^ $ X\neq {\mathrm{succ}}\ ​X $ ^
 === Reference === === Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Successor_ordinal|Successor ordinal]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Successor_ordinal|Successor ordinal]]
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