Divergent Sequence with Finite Number of Terms Deleted is Divergent
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Theorem
Let $\left({X, d}\right)$ be a metric space.
Let $\left \langle {x_k} \right \rangle$ be a sequence in $X$.
Let $\left \langle {x_k} \right \rangle$ be divergent.
Let a finite number of terms be deleted from $\left \langle {x_k} \right \rangle$.
Then the resulting subsequence is divergent.
Proof
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