Monotonicity (What it means for a function to be increasing or decreasing) 

We define what it means for a function to be strictly increasing, weakly increasing, strictly decreasing, or weakly decreasing on a set of arguments. For convenience we define monotonic functions to be the collection of increasing and decreasing functions taken together. We look at several examples, and we also discuss how these definitions have not been universally settled, and we also discuss how a certain tolerance for ambiguity might be allowed in order for discussions to flow freely.