Binary Relation
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Binary Relation
Feb 28, 2021
calcworkshop.com
Let P be a set on which a binary relation < is defined such that, for all x, y, z ∈P, (a) x<x is false, (b) x<y and y<z imply x<z. Prove that if ⩽is defined by x ⩽y ⟺(x<y or x=y), then ⩽is an order on P, and moreover every order on P arises from a relation < satisfying (a) and (b). (A binary relation satisfying (a) and (b) is called a strict order.) | Numerade
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