 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2006/e/e1/b/solution

A sequence converges to

x \in X

when

\forall ε > 0 \exists N \forall n \geq N : d (x_{n}, x) < ε .

The phrase convergent sequence requires the limit to belong to the stated metric space; convergence in a larger ambient space alone does not suffice.

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