Mark Jason Dominus: The road to epsilon-zero: Infinite Nim as a coin-moving game
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals In the previous articles I talked about the game of Nim, a very simple game for two players: There are some piles of beans Players alternate turns A legal move is to take any number of beans from one pile Whoever takes the last bean wins I wrote about how Nim could be extended to include certain types of “infinite” piles while still remaining a sensible game. This involved introducing green tokens that could be replaced with any number of beans, then square tokens that could be…
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