I am reading my course in stochastic process, and the professor defined in the beginning a constant function as an increasing and decreasing function in the same time. Can someone explain me why can't we just say that a constant function is a constant function and it's not monotonic ? "Incresing" & "decreasing" are used by them in a strict or non strict sense ? Thank you
2026-03-29 03:03:46.1774753426
Nature (Monotonicity) of constant function
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Apparently your professor uses "increasing" and "decreasing" in the non-strict sense. I would prefer to say "non-decreasing" and "non-increasing", but not everyone agrees.