Monotone and bounded sequences

Two qualitative properties describe the behaviour of a sequence without computing its limit: monotonicity and boundedness.

Definition — Monotonicity and boundedness

$(a_n)$ is increasing if $a_{n+1}\ge a_n$ for every $n$ (strictly increasing if $>$). It is decreasing if $a_{n+1}\le a_n$. It is monotone if it is increasing or decreasing. It is bounded if there exist $m, M\in\mathbb{R}$ with $m\le a_n\le M$ for every $n$.

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Topics: Sequences
Concepts: Monotonicity · Bounded sequence