Monotonicity

Monotonicity is a property of functions that describes how changes in output are related to changes in input. Consider a function f and the values a and b from the function's domain. The definitions most used in basic reasoning about algorithms with respect to monotonicity are as follows:

Monotonically increasing

a≤b⇒f(a)≤f(b)

Monotonically decreasing

a≤b⇒f(a)≥f(b)

Strictly increasing

a<b⇒f(a)<f(b)

Strictly decreasing

a<b⇒f(a)>f(b)

References

T. H. Cormen, C. E. Leiserson, R. L. Rivest, Introduction to Algorithms. MIT Press, 1990.