Well-quasi-ordering
In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which every infinite sequence of elements x 0 , x 1 , x 2 , … {\displaystyle x_{0},x_{1},x_{2},\ldots } from X {\displaystyle X} contains a non-decreasing pair x i ≤ x j {\displaystyle x_{i}\leq x_{j}} with i < j . {\displaystyle i<j.} == Motivation == Well-founded induction can be used on any set with a well-founded relation, thus one is interested in when a quasi-order is well-founded.