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Definition: Let f be a real-valued function defined on a subset S of R. Then f is said to be increasing (or nondecreasing) on S if for every pair of points x and y in S, x < y implies f(x) <= f(y). If x < y implies f(x) < f(y), then f is said to be strictly increasing on S. (Decreasing functions are similarly defined.) A function is called monotonic on S if it is increasing on S or decreasing on S.
Source: Mathematical Analysis, second edition by Tom M. Apostol