MEX

MEX may refer to:

Mex may refer to:

MeX may refer to:

Mex, Valais

Mex is a former municipality in the district of Saint-Maurice, in the canton of Valais, Switzerland. On 1 January 2013 the former municipality of Mex (VS) merged into the municipality of Saint-Maurice.

History

Mex is first mentioned in 1298 as Meys.

Geography

Before the merger, Mex had a total area of 7.9 km² (3.1 sq mi). Of this area, 1.02 km² (0.39 sq mi) or 12.9% is used for agricultural purposes, while 3.87 km² (1.49 sq mi) or 48.9% is forested. Of the rest of the land, 0.2 km² (0.077 sq mi) or 2.5% is settled (buildings or roads), 0.14 km² (35 acres) or 1.8% is either rivers or lakes and 2.68 km² (1.03 sq mi) or 33.8% is unproductive land.

Of the built up area, housing and buildings made up 0.9% and transportation infrastructure made up 0.6%. Out of the forested land, 42.9% of the total land area is heavily forested and 3.2% is covered with orchards or small clusters of trees. Of the agricultural land, 0.0% is used for growing crops and 2.3% is pastures and 10.6% is used for alpine pastures. All the water in the municipality is flowing water. Of the unproductive areas, 9.5% is unproductive vegetation and 24.4% is too rocky for vegetation.

Mex (mathematics)

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 stones, the nimber is 0 because the mex of the empty set of legal moves is the nimber 0. If n is 1 stone, the player to move will leave 0 stones, and mex({0}) = 1, gives the nimber for this case. If n is 2 stones, the player to move can leave 0 or 1 stones, giving the nimber 2 as the mex of the nimbers { 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 nimbers {0, 1, ..., n-1} is always the nimber n. The first player wins in Nim if and only if the nimber is not zero, so from this analysis we can conclude that the first player wins if and only if the starting number of stones in a one-pile game of Nim is not zero; the winning move is to take all the stones.