Sequence/Different/Accumulation point/Distance/Exercise

Let ${\left(x_n\right)}_{n\in \mathbb{N}}$ be a sequence in a metric space $M$, and suppose that all members are different. Let $A=\{x_n\mid n\in \mathbb{N}\}$, and let $P$ be a point from $M$ different from all members. Show that $P$ is an accumulation point of the sequence if and only if

$d(A,P)=0.$

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