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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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1 Syllable

beck's · becks · blech's · checks · chex · czechs · dec's · decks · derpx · dex · eckes · ex · flecks · flex · heck's · hex · jex · lex · meckes · necks · next · peck's · pecks · phone · plex · rex · sex · sheck's · shek's · six · specks · specs · tech's · techs · teck's · tex · text · treks · vex · wrecks · x · xxx

2 Syllables

annex · caltex · cmx · complex · convex · disex · execs · expects · fanech's · nobec's · onex · perplex · pretext · quebec's · reflects · regrets · rejects · success · wall-tex

3 Syllables

atx · googolplex · govpx · megaplex

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mex#10000#21339#100000

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"mex Rhymes." Rhymes.net. STANDS4 LLC, 2019. Web. 22 Jul 2019. <https://www.rhymes.net/rhyme/mex>.

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