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cards-deck: default_obsidian
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## monotone
$a_{n}<a_{n}+1$ increasing
$a_{n}>a_{n}+1$ decreasing

Can be used to define limits.

## Bounds

### bounded above
There is a $M$ such that $a_{n}\le M$ for all $n>1$

### bounded below
There is a $m$ such that $a_{n}\ge m$ for all $n>1$

## monotone and bounded convergent
Definition of 'bounded' ::: Bounded from both above and below.  ^1653317426701
You have to specify if it's just above or just below.

The [[sequences|sequence]] is [[convergence and divergence of series.|convergent]] if it's monotone + bounded in its direction, or if it's generally monotone+bounded.