A function f(n) is monotonically increasing, if m ≤ n implies f(m) ≤ f(n).
Conversely, it is monotonically decreasing if m ≥ n implies f(m) ≥ f(n).[1]
A function f(n) is strictly increasing, if m < n implies f(m) < f(n).
Conversely, it is strictly decreasing if m > n implies f(m) > f(n).[1]