The road to epsilon-zero: Coin-moving games with no coins

Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game In the previous article we saw how to interpret Nim heaps of up to beans as coins on a quarter-infinite array: The coin here represents a heap of beans. The heap can be reduced to any smaller number of beans. In the coin version of the game, this…