Convergent Sequence in Metric Space has Unique Limit/Proof 2
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Theorem
Let $M = \struct {A, d}$ be a metric space.
Let $\sequence {x_n}$ be a sequence in $M$.
Then $\sequence {x_n}$ can have at most one limit in $M$.
Proof
We have that a Metric Space is Hausdorff.
The result then follows from Convergent Sequence in Hausdorff Space has Unique Limit‎.
$\blacksquare$