MathItems

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 $\varepsilon>0$ there is an integer $N$ such that $n\geq N$ implies that $d(p_n,p)<\varepsilon$. (Here $d$ denotes the distance in $X$.)

In this case we also say that $\{p_n\}$ converges to $p$.