Why Nim Games with Infinite Ordinals Must Always End

The road to epsilon-zero: Nim always ends, even with infinite ordinals

I explore how the game of Nim remains finite even when played with infinite ordinal numbers like omega. Although we cannot predict the exact duration of such games, the well-founded nature of ordinals guarantees that every move reduces the game state, ensuring it must eventually terminate at zero. This mathematical principle mirrors the challenge of estimating complex programming tasks, where knowing when an estimate will be ready is sometimes the only certainty.