Post

The distinction between the strict and non-strict version is useful, sure. For instance in analysis, any continuous monotone function is differentiable a.e. But its derivative is never zero if strictly increasing, while the Cantor function, which is non-strictly increasing, has zero derivative a.e.

The sine function is also not increasing, though ;-) I suppose there are just often many names for the same thing, but perhaps the origins are from different (sub-) fields? I actually like non-decreasing as I find it less ambiguous than increasing (which can be confused with strictly increasing).

In French, we say increasing and strictly increasing. The non-decreasing thing always sounded weird to me. I suspect it is also the cause of many many translation errors.

Yeah, why not? I was taught "non-decreasing" and mostly never questioned it, but really "non-strictly increasing" seems better.

That's the first time I hear it like that!

in my experience convex is rarely, if ever, used in day to day life. most people who arent mathematicians seem unsure of the difference between concave and convex to begin with. not apples to apples imo since increasing is used by everyone pretty regularly, with an agreed upon meaning.