Is a sequence a subsequence of itself? I don't think it is but am not really sure.

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- Feb 21st 2010, 04:05 PMmesmoSequence and Subsequence Concept Question
Is a sequence a subsequence of itself? I don't think it is but am not really sure.

- Feb 21st 2010, 04:51 PMpatrick
Sure, just as a set is a subset of itself.

- Feb 21st 2010, 06:37 PMDrexel28
Agreed. Let $\displaystyle \varphi:\mathbb{N}\mapsto\mathbb{N}$ be monotonically increasing then we call $\displaystyle \left\{x_{\varphi(n)}\right\}$ a subsequence of $\displaystyle \{x_n\}$. Try taking $\displaystyle \varphi(n)=n$ (Evilgrin)