Math and science::Analysis::Tao::06. Limits of sequences

# Monotone bounded sequences converge

#### Increasing, decreasing and monotone

A sequence \( (a_n)_{n=0}^{\infty} \) is *increasing*
if \( a_n \le a_{n+1} \) for all \( n \in \mathbb{N} \) and *decreasing*
if \( a_n \gt a_{n+1} \) for all \( n \in \mathbb{N} \). A sequence is
*monotone* if it is either increasing or decreasing.

### Monotone bounded sequences converge

If a sequence is [...] and [...], then it converges.