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For a set of positive integers, its minimum excluded positive integer is the least positive integer absent from the set. This is the positive-indexed version of the minimum excludant, which normally allows zero.

Sprague-Grundy theory studies finite acyclic impartial games under the normal-play convention by assigning each position a Grundy number. The assignment recursively takes the minimum excludant of the values of all legal followers. The Sprague-Grundy theorem then reduces a disjunctive sum of games to the bitwise exclusive or of its component values. This framework explains both why a zero value is losing and how independently understood games can be combined without exploring the entire product of their state spaces.