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Every Preorder Relation induces an Order Relation

Last updated Nov 1, 2022

# Statement

Let (P,R)(P, R) be a Preorder

Preorder

Definition Let PP be a and let RR be a on PP. Then (P,R)(P, R) is a ....

11/7/2022

. Then there exists an Equivalence Relation

Equivalence Relation

Definition Let XX be a and let R⊂X×XR \subset X \times X be a on XX. Then RR is...

11/7/2022

∼\sim on PP so that (P/∼,R/∼)(P/\sim,R/\sim) is a Partial Ordering

Partial Ordering

Definition Let PP be a and let ≤\leq be an on PP. Then (P,≤)(P, \leq) is a . Remarks We can...

11/7/2022

.

# Proof

Backlinks

  • Order Relation

    Order Relation

    ...Let PP be a and let R⊂P×PR \subset P \times P be a on PP. Then RR is an if RR is a and the following holds: Antisymmetry: Let x,y∈Px, y \in P. If xRyxRy and......

    11/7/2022

Interactive Graph

Every Preorder Relation induces an Order RelationPreorderEquivalence RelationPartial OrderingOrder Relation