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 an increasing pair x i ≤ x j {\displaystyle x_{i}\leq x_{j}} with i < j. Wikipedia