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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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