View source for Subsequence/Definition

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==Definition==
</noinclude>Given a sequence {{M|1=(x_n)_{n=1}^\infty}} we define a ''subsequence of {{M|1=(x_n)^\infty_{n=1} }}''{{rAPIKM}} as a sequence:
* {{M|k:\mathbb{N}\rightarrow\mathbb{N} }} which operates on an {{M|n\in\mathbb{N} }} with {{M|1=n\mapsto k_n:=k(n)}} where:
** {{M|k_n}} is increasing, that means {{M|k_n\le k_{n+1} }}

We denote this:
* {{M|1=(x_{k_n})_{n=1}^\infty}}<noinclude>
==References==
<references/>
{{Definition|Set Theory|Real Analysis|Functional Analysis}}
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