ordering of games

Path: <= CGT path =>
    Keywords: Theory

This is a foundational concept of CGT.

In terms of the game 0, one can proceed by defining what it means to have G >= 0, for any game G. This means that Left can win G, if Right starts.

Since one expects that G >= H will mean that G - H >= 0, one can make that the definition (here G - H is the construction of the difference game).

Games are only partially ordered, since two games may not be comparable at all with respect to the order. If a game is a first player win, it is fuzzy, that is, not greater than or less than 0, nor equal to 0. If games G and H are such that G - H is fuzzy, we can't use the order relation to compare G with H.

Path: <= CGT path =>
ordering of games last edited by xela on November 4, 2007 - 12:57
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