Arguably one of the most hated parts of English mathematical terminology is the word “nondecreasing”, referring to a function such that $x\leq y \;\Rightarrow\; f(x)\leq f(y)$ (what other conventions or languages might call something like “weakly increasing”, “(weak-)order-preserving” or various variations thereof). The term is much hated, of course, because it is not the negation of “decreasing” (i.e., there are functions which are not decreasing but neither are they nondecreasing), so the question arises as to how this annoyance came about.
I can form two (noncontradictory!) conjectures as to the origin of “nondecreasing”:
One is that it is simply formed by analogy with “nonnegative” to mean “$\geq 0$” (which is also questionable, but at least makes sense logically) and “no less” to mean “$\geq$”: simply following the same pattern of using “non-” with the reversed inequality gives “nondecreasing”.
Another is that “nondecreasing” should really be “monotonically nondecreasing” (some people indeed use the full form, which is cumbersome but clear), and that the adverb was eventually left out as it seemed redundant (rather than being later added by people who wanted to make the term less illogical).
Question: Who introduced “nondecreasing”, when, and why? And is either (or both) of the above conjectures correct?