Partially ordered set


 
 

In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation. This relation formalizes the intuitive concept of an ordering, sequencing, or arrangement of that set's elements. Such an ordering does not necessarily need to be total, that is, it need not guarantee the mutual comparability of all objects in the set.

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A partial order is a binary relation R over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b and c in P, we have that:

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~ Table of Content ~

Introduction
Formal definition
Examples
Strict and weak partial orders
Category theory
See also
 


 

~ Related Subjects ~

Set (2) - Binary relation (2) - Mathematics (2) - Order theory glossary (1) - Mathematic (1) - Set (disambiguation) (1) - List of order topics (1) - Transitive (1) - Total (1) - Order theory (1) - Antisymmetric (1) - Reflexive (1) -
 

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