The road to epsilon-zero: Productive programs and well-founded orders

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 Coin-moving games without the coins Previously we saw how to interpret the difficult-seeming ordinal as a particular ordering of the set of finite sequences of numbers, revealing what seemed like a scary monster as gentle and straightforward. Now…