Subsequence
Concept history
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Revision 826
8/2/2026, 7:18:41 AM · Sequoia
Concept edited
Recorded titleSubsequence
Recorded typeDefinition
Compare with revision 6702 changed lines
1
Let $(a_{n})_{n\in \N}$ be a [[Sequence|sequence]] in a set $X$. A subsequence of $(a_{n})$ is a sequence of the form2
$$(a_{n_{k}})_{k\in \N}$$3
where $(n_{k})$ is a [[strictly increasing sequence|strictly increasing sequence]] of [[Natural number|natural numbers]].4
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Sometimes, one also uses the notation $(a_{\varphi(n)})_n$ where $\varphi(n)\colon\N\to\N$ is a strictly increasing function called "extractor".Revision 670
7/27/2026, 1:02:55 PM · Ancient Tree
Concept created
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]].