Monotone sequence - Imported Knowlpedia Content

A monotone sequence is a sequence $(a_n)_{n\ge 1}$ of real numbers such that either

$a_n\le a_{n+1}$ for all $n$ (monotone increasing), or
$a_n\ge a_{n+1}$ for all $n$ (monotone decreasing).

Remarks

A sequence can be viewed as a function from $\mathbb N$ to $\mathbb R$ . Monotone sequences are central in the monotone sequence convergence theorem, which combines monotonicity with being bounded above or bounded below.

Examples

$a_n=1-\tfrac1n$ is monotone increasing.
$a_n=\tfrac1n$ is monotone decreasing.