A ==Poset== (Partially Ordered Set) is a pair (P, $\leq$) where P is a set and $\leq$ is a binary relation on P that satisfies three properties; Reflexivity, Antisymmetry, and Transitivity. $\forall x \in P, x \leq x$ $\forall x,y \in P \quad \text{if} \quad x \leq y \quad \\ \text{and} \quad y \leq x, \quad \text{then} \quad x = y $