Monotonicity refers to the property of a function or sequence that consistently increases or decreases without changing direction. A function is considered monotonic increasing if, for any two points, the value at the second point is greater than or equal to the value at the first. Conversely, a function is monotonic decreasing if the value at the second point is less than or equal to the value at the first. In mathematics, monotonicity is important for understanding the behavior of functions and sequences. It helps in analyzing limits, derivatives, and integrals. Monotonic functions are often easier to work with, as they do not exhibit oscillations or fluctuations, making them predictable in their behavior.