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 a1 \in A < a2 \in A, f(a1) <= f(a2). If the inequality is strict, f is said to be strictly monotonically increasing.
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