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 $\sequence {x_n}$.

In string theory, x is a subsequence of y if x can be derived from y by deleting some or no characters without changing the order of the remaining elements (like substring, but subsequences are not required to occupy consecutive positions within the original sequences), for example, bce is a subsequence of abcdef, while cfd is not.

Also see

 * Definition:Sequence
 * Definition:Subsequential Limit