> **Puzzle 8.** What simple law do Daniel's preorders obey, that does not hold for the real numbers with its usual notion of \$$\leq\$$?

Both obey the *symmetry* rule: if \$$x \leq y\$$ then \$$y \leq x\$$

> **Puzzle 9.** What do you call preorders that obey this law?

They are [*equivalence relations*](https://en.wikipedia.org/wiki/Equivalence_relation).