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Can you help me with something:

Players alternately choose 0's or 1's. A play of this infinite game is thus a sequence of 0's and 1's. Such a sequence can be considered as the binary expansion of a real number between 0 and 1. Given a set ##E## of real numbers satisfying ##0 < x < 1 \forall x \in E##, say that player 1 wins if the play corresponds to a number in ##E## and player two wins if the way corresponds to a number in ##[0,1] \backslash E##.

Evidently the Axiom of Choice implies there exists a set ##E## for which the game has no value. Can you help me out with showing this?

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# Game Theory Question

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