Squeeze Theorem/Sequences/Metric Spaces

Theorem
Let $M = \struct {S, d}$ be a metric space or pseudometric space.

Let $p \in S$.

Let $\sequence {r_n}$ be a null sequence in $\R$.

Let $\sequence {x_n}$ be a sequence in $S$ such that:


 * $\forall n \in \N: \map d {p, x_n} \le r_n$.

Then $\sequence {x_n}$ converges to $p$.

Proof
Thus $\sequence {x_n}$ converges to $p$.