quartz/content/vault/monotone_and_bounded.md

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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 is convergence and divergence of series. if it's monotone + bounded in its direction, or if it's generally monotone+bounded.