Partial order (poset)

Parent: basic-orders

Partial order

A preorder that is also antisymmetric (a≤b ∧ b≤a ⟹ a=b). Distinct elements may still be incomparable.

Incomparability is the whole point — a poset is drawn as a Hasse diagram (put a below b with an edge when a<b and nothing sits strictly between — draw only the covers; reflexive/transitive edges are implied):

{a} and {b} are incomparable — that's why inclusion is partial, not total. Examples: ⊆ on sets, divisibility | on ℕ (antisymmetric here), the componentwise order on ℝⁿ, the subtyping order.