# Differences

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 loop [2013/08/06 21:42]nikolaj created loop [2014/03/21 11:11] (current) 2013/08/06 21:48 nikolaj 2013/08/06 21:42 nikolaj created Next revision Previous revision 2013/08/06 21:48 nikolaj 2013/08/06 21:42 nikolaj created Line 1: Line 1: ===== Loop ===== ===== Loop ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $X$ | + | @#55CCEE: context ​    | @#55CCEE: $X$ | - | @#55EE55: $\langle X,* \rangle \in \text{Loop}(X)$ | + | @#55EE55: postulate ​  | @#55EE55: $\langle X,* \rangle \in \text{Loop}(X)$ | - | @#88DDEE: $\langle X,* \rangle \in \mathrm{Quasigroup}(X)$ | + | @#55CCEE: context ​    | @#55CCEE: $\langle X,* \rangle \in \mathrm{Quasigroup}(X)$ | - | @#DDDDDD: $a,a^{-1}\in X$ | + | @#DDDDDD: range       | @#DDDDDD: $e,a\in X$ | - | @#55EE55: $\forall a.\ \exists ​a^{-1}.\ (a*a^{-1}=a^{-1}*a=e)$ | + | @#55EE55: postulate ​  | @#55EE55: $\exists e.\ \forall ​a.\ (a*e=e*a=a)$ | Here we used infix notation for "​$*$"​. Here we used infix notation for "​$*$"​. Line 23: Line 23: ==== Reference ==== ==== Reference ==== Wikipedia: [[http://​en.wikipedia.org/​wiki/​Quasigroup|Quasigroup]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Quasigroup|Quasigroup]] - ==== Context ​==== + ==== Parents ​==== === Subset of === === Subset of === [[Quasigroup]] [[Quasigroup]]