Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
successor_set [2013/09/16 10:48] nikolaj |
successor_set [2014/03/27 10:58] nikolaj |
||
---|---|---|---|
Line 1: | Line 1: | ||
===== Successor set ===== | ===== Successor set ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
- | + | | @#FFBB00: definiendum | @#FFBB00: $ S(X) \equiv X \cup \{X\} $ | | |
- | | @#FFBB00: $ S(X) \equiv X \cup \{X\} $ | | + | |
==== Discussion ==== | ==== Discussion ==== | ||
=== Theorems === | === Theorems === | ||
^ $ X\in S(X) $ ^ | ^ $ X\in S(X) $ ^ | ||
- | ^ $ (S(X)=S(Y))\implies (X=Y) $ ^ | + | ^ $ (S(X)=S(Y))\Rightarrow (X=Y) $ ^ |
- | ^ $ (Y\in S(X))\iff (Y=X\lor Y=\{X\}) $ ^ | + | ^ $ (Y\in S(X))\Leftrightarrow (Y=X\lor Y=\{X\}) $ ^ |
^ $ X\neq S(X) $ ^ | ^ $ X\neq S(X) $ ^ | ||
=== Reference === | === Reference === |