subsequence

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Definition

Let $(a_n)$ be a sequence of real numbers, and let $n_1 < n_2 < n_3 < \cdots$ be an increasing sequence of natural numbers. Then the sequence $(a_{n_1}, a_{n_2}, a_{n_3}, \ldots)$ is called a subsequence of $(a_n)$ and is denoted by $(a_{n_k})$.