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Partial Order

Partial Order

Jun 11, 20251 min read

algebra

Definition

Partial Order

A relation R is a partial order if the following properties are fulfilled:

  • reflexive: ∀a:aRa
  • antisymmetric: ∀a,b:aRb∧bRa⟹a=b
  • transitive: ∀a,b,c:aRb∧bRc⟹aRc

Example:

aRb:⟺a≤b

A partial order is called total order if ∀a,b:aRb∨bRa.


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