Editing Sequence (section)

===Increasing and decreasing===
A sequence is said to be ''monotonically increasing'' if each term is greater than or equal to the one before it. For example, the sequence <math display=inline>{(a_n)}_{n=1}^{\infty} </math> is monotonically increasing if and only if <math display=inline>a_{n+1} \geq a_n</math> for all <math>n \in \mathbf N.</math> If each consecutive term is strictly greater than (>) the previous term then the sequence is called '''strictly monotonically increasing'''. A sequence is '''monotonically decreasing''' if each consecutive term is less than or equal to the previous one, and is '''strictly monotonically decreasing''' if each is strictly less than the previous. If a sequence is either increasing or decreasing it is called a '''monotone''' sequence. This is a special case of the more general notion of a [[monotonic function]].

The terms '''nondecreasing''' and '''nonincreasing''' are often used in place of ''increasing'' and ''decreasing'' in order to avoid any possible confusion with ''strictly increasing'' and ''strictly decreasing'', respectively.