Convergent Real Sequence has Unique Limit/Proof 2
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Theorem
Let $\sequence {s_n}$ be a real sequence.
Then $\sequence {s_n}$ can have at most one limit.
Proof
We have that the real number line is a metric space
The result then follows from Convergent Sequence in Metric Space has Unique Limit‎.
$\blacksquare$