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Partial Order

Definition: A binary relation on S is a partial order, if it is reflexive, antisymmetric, and transitive:

R is partial order on S : <=>

R subset S x S /\

R is reflexive on S /\

R is antisymmetric on S /\

R is transitive on S.

Example:

• subset  is a partial order on P(S), for every set S.
• | (divides) is a partial order on N.