## FANDOM

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

## Formal definition

Let $\le$ be a binary relation on $X$.

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

1. $\forall x \in X (x \le x)$ (The binary relation is reflexive).
1. $\forall x,y \in X ((x \le y \land y \le x) \Rightarrow x=y)$ (The binary relation is antisymmetric).
1. $\forall x,y,z \in X ((x \le y \land y \le z) \Rightarrow x \le z)$ (The binary relation is transitive)
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