Find another monoidal monotone different from the one defined in Eq. 2.66.

Consider We have already shown (Ex. 2.44) that g is a monoidal monotone. Thus, g can turn a Lawvere metric space into a preorder. Intuitively, the preorder relationship will be the one of "reachability": if and only if can be reached from in a finite time going at a finite velocity.