Note to definition of Increasing and Decreasing functions

Some textbooks say that a function g is increasing if for all u and v in I, $g(u) \le g(v)$ whenever $u \lt v$ and say that a function is decreasing if for all u and v in I, $g(u) \ge g(v)$ whenever $u \lt v$. These definitions allow a constant function to be both increasing and decreasing.

These textbooks would use the terms strictly increasing and strictly decreasing for what we've defined as increasing and decreasing functions.