# Sequence and Subsequence Concept Question

• February 21st 2010, 04:05 PM
mesmo
Sequence and Subsequence Concept Question
Is a sequence a subsequence of itself? I don't think it is but am not really sure.
• February 21st 2010, 04:51 PM
patrick
Sure, just as a set is a subset of itself.
• February 21st 2010, 06:37 PM
Drexel28
Quote:

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

Quote:

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 $\varphi(n)=n$ (Evilgrin)