Real numbers/Subsequence/Definition

Subsequence

Let ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a real sequence. For any strictly increasing mapping ${}\mathbb {N} \rightarrow \mathbb {N} ,i\mapsto n_{i}$, the sequence

$i\mapsto x_{n_{i}}$

is called a subsequence of the sequence.