Is a sequence a subsequence of itself? I don't think it is but am not really sure.
Originally Posted by patrick
Sure, just as a set is a subset of itself.
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 $\displaystyle \varphi(n)=n$