---
type: "concept"
title: "Subsequence"
slug: "subsequence"
language: "en"
translationGroupId: "cms38lyun000bqq01h1ijqa1g"
domain: "Set theory"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

Let $(a_{n})_{n\in \N}$ be a [[Sequence|sequence]] in a set $X$. A subsequence of $(a_{n})$ is a sequence of the form
$$(a_{n_{k}})_{k\in \N}$$
where $(n_{k})$ is a [[strictly increasing sequence|strictly increasing sequence]] of [[Natural number|natural numbers]].