In the current version of my book (related with order theory) I used the term monotone to denote $\forall x,y:(x\geq y\Rightarrow f(x)\geq f(y))$.
Should this usage of the term monotone be considered correct, or should the term increasing be used instead?
If I switch to the term increasing, how to reformulate such phrase as "Monotonicity is obvious." or "by monotonicity of composition"?