Many fixed points, one least
Add one more rule that is also true (N is odd when N + 1 is even):
Now the rules have two fixed points over num = {0, …, 5}:
even | odd | ||
|---|---|---|---|
| ① | {0, 2, 4} | {1, 3, 5} | all facts tracing back to even(0) |
| ② | {0, 1, 2, 3, 4, 5} | {0, 1, 2, 3, 4, 5} | ”extra” facts support each other |
① is contained in ②, in fact it is the least fixed point, our intended answer.