# Thread: Sequence and Subsequence Concept Question

1. ## Sequence and Subsequence Concept Question

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

2. Sure, just as a set is a subset of itself.

3. Originally Posted by mesmo
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 $\varphi:\mathbb{N}\mapsto\mathbb{N}$ be monotonically increasing then we call $\left\{x_{\varphi(n)}\right\}$ a subsequence of $\{x_n\}$. Try taking $\varphi(n)=n$