A partial order is a binary relation that is reflexive, antisymmetric, and transitive.

Formal definition

Let ${\displaystyle \le}$ be a binary relation on ${\displaystyle X}$.

Then, ${\displaystyle \le}$ is a partial order on ${\displaystyle X}$ if the following holds:

1. ${\displaystyle \forall x \in X (x \le x)}$ (The binary relation is reflexive).

1. ${\displaystyle \forall x,y \in X ((x \le y \land y \le x) \Rightarrow x=y)}$ (The binary relation is antisymmetric).

1. ${\displaystyle \forall x,y,z \in X ((x \le y \land y \le z) \Rightarrow x \le z)}$ (The binary relation is transitive)