> **Puzzle 16**. What's going on here? What's the pattern you see, and why is it working this way?

I'm not sure if this is the answer you want John...

I want to expand on Alex Kreitzberg's observation. He is touching on an _alternate definition_ of a Galois pair \\(f \dashv g\\):

$$
f \text{ and } g \text{ are monotone functions and } f(g(b)) \leq b \text{ and } a \leq g(f(a))
$$

This is equivalent to the definition Fong, Spivak and you yourself use.

Moreover, if a monotone function has a left (or right) Galois adjoint it is unique.