A real function or sequence is called monotonic if it either constantly increases or decreases. Thus, the sequence of powers of 2 is monotonically increasing because each term is larger than the previous. The function is monotonically decreasing on the interval and monotonically increasing on the interval . However, the function is not monotonic over the entire real line because it sometimes increases and sometimes decreases.
More formally, a function is monotonically increasing (resp. decreasing) if (resp. . The function is strictly monotonic if, in addition, .