The road to epsilon-zero: ordinals as nim-heaps

Previously: Ordinal numbers and basic set theory We're going to get to in a long and roundabout way. First I want to talk about the game of Nim. Nim Nim is a very simple game for two players. There are some piles of beans, which are called nim-heaps . When it's your turn, you are allowed to remove as many beans as you like, as long as they are all in the same pile. Whoever takes the last bean…