- Nim with ω-tokens always ends because ordinals are well-founded, ensuring a finite sequence of moves.
- Even with infinite ordinals like ω·2, the game must eventually end, though we cannot predict exactly when.
- Well-foundedness means every decreasing sequence of ordinals reaches zero in finite steps.
- This property is analogous to recursion termination in programming, where arguments must shrink.
- A story about programmer estimates illustrates ω·2+1: the inability to estimate but certainty of eventual completion.