A sequence $\{p_n\}$ in a metric-space $X$ is said to converge if there is a point $p \in X$ with the following property: For every $\epsilon > 0,$ there is an integer $N$ such that $n \geq N$ implies that $d(p_n, p) < \epsilon.$

If a sequence $\{p_n\}$ converges to $p,$ we say that $p$ is the limit of $\{p_n\},$ denoted as:

$$ \lim_{n \to \infty} p_n = p. $$

If a sequence $\{p_n\}$ does not converge, it is said to diverge.

The set of all points $p_n$ of a sequence $\{p_n\} (n = 1, 2, 3, \dots)$ is the range of $\{p_n\}.$

The sequence $\{p_n\}$ is said to be bounded if its range is bounded.