# 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.