MathGloss

A partially ordered set is a set $X$ together with a homogeneous relation $\leq$ such that for all $x,y,z\in X$,

1. $\leq$ is reflexive, i.e. $x\leq x$;
2. $\leq$ is antisymmetric, i.e. if $x\leq y$ and $y\leq x$ then $x=y$;
3. $\leq$ is transitive, i.e. if $x\leq y$ and $y\leq z$ then $x\leq z$.

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