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 $a_{n} \leq a_{n + 1}$ for all $n \in N$ and decreasing if $a_{n} > a_{n + 1}$ for all $n \in N$ . A sequence is monotone if it is either increasing or decreasing.

Monotone bounded sequences converge

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

The easiest card ever. The proof is on the reverse; can you think of it? The proof is easy and obvious in retrospect, but it uses a property that I originally didn't consider using to solve the problem.

22.02.2021