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In mathematics, the binary game is a topol … In mathematics, the binary game is a topological game introduced by Stanislaw Ulam in 1935 in an addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game. In the binary game, one is given a fixed subset X of the set {0,1}N of all sequences of 0s and 1s. The players take it in turn to choose a digit 0 or 1, and the first player wins if the sequence they form lies in the set X. Another way to represent this game is to pick a subset of the interval on the real line, then the players alternatively choose binary digits . Player I wins the game if and only if the binary number , that is, . See, page 237. The binary game is sometimes called Ulam's game, but "Ulam's game" usually refers to the Rényi–Ulam game.me" usually refers to the Rényi–Ulam game.
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| rdfs:comment |
In mathematics, the binary game is a topol … In mathematics, the binary game is a topological game introduced by Stanislaw Ulam in 1935 in an addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game. In the binary game, one is given a fixed subset X of the set {0,1}N of all sequences of 0s and 1s. The players take it in turn to choose a digit 0 or 1, and the first player wins if the sequence they form lies in the set X. Another way to represent this game is to pick a subset of the interval on the real line, then the players alternatively choose binary digits . Player I wins the game if and only if the binary number , that is, . See, page 237. binary number , that is, . See, page 237.
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| rdfs:label |
Binary game
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