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 $\sequence {x_n}$.

Also see

 * First Subsequence Rule
 * Limit of Subsequence equals Limit of Sequence
 * Divergent Sequence may be Bounded