Set/Order relation/Definition

Order relation

A relation ${}\preccurlyeq$ on a set ${}I$ is called an order relation, if the following three conditions are fulfilled.

1. ${}i\preccurlyeq i$ for all ${}i\in I$.
2. From ${}i\preccurlyeq j$ and ${}j\preccurlyeq k$ we can deduce ${}i\preccurlyeq k$.
3. From ${}i\preccurlyeq j$ and ${}j\preccurlyeq i$ we can deduce ${}i=j$.