Definition:Subsequence

Definition
Let $\sequence {x_n}$ be a sequence in a set $S$.

Let $\sequence {n_r}$ be a strictly increasing sequence in $\N$.

Then the composition $\sequence {x_{n_r} }$ is called a subsequence of $\sequence {x_n}$.

Also see

 * Definition:Sequence
 * Definition:Subsequential Limit