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 successor_set [2014/03/27 10:58]nikolaj successor_set [2014/12/05 10:51] (current)nikolaj Both sides previous revision Previous revision 2014/12/05 10:51 nikolaj 2014/03/27 10:58 nikolaj 2014/03/27 10:57 nikolaj 2014/03/21 11:11 external edit2013/09/16 10:48 nikolaj 2013/09/16 10:48 nikolaj 2013/09/06 22:04 external edit2013/09/05 21:40 nikolaj 2013/09/05 21:39 nikolaj 2013/09/05 19:32 nikolaj 2013/09/02 19:49 nikolaj 2013/08/23 20:51 nikolaj 2013/08/23 20:47 nikolaj 2013/08/23 20:46 nikolaj 2013/08/23 20:43 nikolaj 2013/05/18 12:56 external edit2013/05/18 00:54 nikolaj created 2014/12/05 10:51 nikolaj 2014/03/27 10:58 nikolaj 2014/03/27 10:57 nikolaj 2014/03/21 11:11 external edit2013/09/16 10:48 nikolaj 2013/09/16 10:48 nikolaj 2013/09/06 22:04 external edit2013/09/05 21:40 nikolaj 2013/09/05 21:39 nikolaj 2013/09/05 19:32 nikolaj 2013/09/02 19:49 nikolaj 2013/08/23 20:51 nikolaj 2013/08/23 20:47 nikolaj 2013/08/23 20:46 nikolaj 2013/08/23 20:43 nikolaj 2013/05/18 12:56 external edit2013/05/18 00:54 nikolaj created Line 2: Line 2: ==== 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]]