# Definition:Subsequential Limit

## Definition

Let $\sequence {x_n}$ be a sequence.

Let $\sequence {x_{n_r} }$ be a subsequence of $\sequence {x_n}$.

Suppose that $\sequence {x_{n_r} }$ converges to a limit $x$.

Then $x$ is called a subsequential limit of $\sequence {x_n}$.