Subsequence

Last updated Nov 1, 2022

Let $f: \mathbb{N} \to X$ be a Sequence on $X$. Let $g: \mathbb{N} \to \mathbb{N}$ be an Increasing Function. Then $g \circ f$ is a Subsequence of $f$.

Oftentimes if $(a_{n}) \subset X$ is the sequence and $(n_{k}) \subset \mathbb{N}$ is the increasing function (i.e. $g$), then $(a_{n_{k}})$ is our subsequence.

1. Pugh - Real Mathematical Analysis - Ch 2, pg unknown