Definition:Monotone (Order Theory)/Sequence/Real Sequence

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Definition

Let $\sequence {x_n}$ be a sequence in $\R$.


Then $\sequence {x_n}$ is monotone if and only if it is either increasing or decreasing.


Also known as

This can also be called a monotonic sequence.


Examples

Example: $\sequence {\paren {-1}^n}$

The first few terms of the real sequence:

$S = \sequence {\paren {-1}^n}_{n \mathop \ge 1}$

are:

$-1, +1, -1, +1, \dotsc$


$S$ is not monotone, either increasing or decreasing.


Also see


Sources