===== Loop =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |

| @#55EE55: postulate   | @#55EE55: $ \langle X,* \rangle \in \text{Loop}(X)$ |

| @#55CCEE: context     | @#55CCEE: $\langle X,* \rangle \in \mathrm{Quasigroup}(X)$ |
| @#DDDDDD: range       | @#DDDDDD: $e,a\in X$ |

| @#55EE55: postulate   | @#55EE55: $\exists e.\ \forall a.\ (a*e=e*a=a) $ |

Here we used infix notation for "$*$".

==== Ramifications ====
=== Discussion ===

The binary operation is often called //multiplication//.

The axioms $*\in \mathrm{binaryOp}(X)$ above means that a monoid is closed with respect to the multiplication. 

One generally calls $X$ the loop, i.e. the set where the operation "$*$" is defined on.

==== Reference ====
Wikipedia: [[http://en.wikipedia.org/wiki/Quasigroup|Quasigroup]]
==== Parents ====
=== Subset of ===
[[Quasigroup]]