Mex (Mathematics)

In mathematics, the mex, or minimum excluded value, of a subset of a well-ordered set is the smallest value in the whole set that does not belong to the subset, that is, the minimum value of the subset's complement; the notion extends beyond sets to subclasses of well-ordered classes, including subclasses of the ordinal numbers. Minimum excluded values are used in combinatorial game theory to assign nim-values to impartial games, since the Sprague-Grundy theorem defines the nim-value of a game position as the mex of the values of every position reachable from it in a single move, and they are also used in graph theory's greedy coloring algorithms, where each vertex in turn is assigned the mex of the colors already used by its neighbors. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/