# What does MEX stand for?

## What does MEX mean? This page is about the various possible meanings of the acronym, abbreviation or slang term: MEX.

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 MEX CBOE (Chicago Board Options Exchange) Mexico Index MEX Dynamically linked subroutines (Macintosh) (Matlab) MEX Macro Editor expound file (WordPerfect Library) MEX Mexican MEX Mexican food MEX Mexico MEX Mexico City, Mexico

#### What does MEX mean?

Mex
In combinatorial game theory, the mex, or "minimum excludant", of a set of ordinals denotes the smallest ordinal not contained in the set. Some examples: where ω is the limit ordinal for the natural numbers. In the Sprague-Grundy theory the minimum excluded ordinal is used to determine the nimber of a normal-play impartial game, which is a game in which either player has the same moves in each position and the last player to move wins. The nimber is equal to 0 for a game that is lost immediately by the first player, and is equal to the mex of the nimbers of all possible next positions for any other game. For example, in a one-pile version of Nim, the game starts with a pile of n stones, and the player to move may take any positive number of stones. If n is zero, the nimber is 0. If n is 1, the player to move will leave 0 stones, and the mex of { 0 }, 1, gives the nimber for this case. If n is 2, the player to move can leave 0 or 1 stones, giving 2 as the mex of { 0, 1 }. In general, the player to move with a pile of n stones can leave anywhere from 0 to n-1 stones; the mex of the numbers { 0, 1, ..., n-1 } is always n. From this we can conclude that the first player wins if n is not zero.

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