Let f be real on (a,b). f is monotone increasing if on (a,b), a< x < y <b implies f(x)less then or equal to f(y)

Let f: A -> B, where A and B are totally ordered. Then f is said to be monotonically increasing if, whenever a_{1} \in A < a_{2} \in A, f(a_{1}) <= f(a_{2}). If the inequality is strict, f is said to be strictly monotonically increasing.

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