Subsequences

Why

We want to select particular terms of sequence.

\ssection{Definition} A subindex is a monotonically increasing function from and to the natural numbers. Roughly, it selects some ordered infinite subset of natural numbers. A subsequence of a first sequence is any second sequence which is the composition of the first sequence with a subindex.

\ssection{Notation}

Let $i: \N \to \N $ such that $n < m \Rightarrow i(n) < i(m)$. Then $i$ is a subindex. Let $b = a \comp i$. Then $b$ is a subsequence of $a$. We denote it by $\set{b_{i(n)}}_n$ and the $n$th term by $b_{i(n)}$.

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