What is a monotonic sequence?

A monotonic sequence is a mathematical term that refers to a function that preserves a given order between ordered sets. For a sequence to qualify as being monotonic, it must always decrease or increase progressively.

To establish whether or not an equation in a series is monotonic, the differential must be found. If the differential value is always decreasing (positive) or increasing (negative), then the sequence is monotonic. However, if some of the differential values are positive while others are negative, then the series is not monotonic. The sequence is most often used in probability theory as it has a limit at either the negative or positive infinity of a real number.