Strict ordering


Definition

A binary relation \(\mathrel{R}\), on a set \(S\), is an ordering if and only if:

\(\mathrel{R}\) is asymmetric:
\(\forall x,y \in S : x{\mathrel{R}}y \Rightarrow \neg(y{\mathrel{R}}x)\)
\(\mathrel{R}\) is transitive:
\(\forall x,y,z \in S : x{\mathrel{R}}y \wedge y{\mathrel{R}}z \Rightarrow x{\mathrel{R}}z\)