 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2007/e/1/a/solution

x \in X

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

The limit must belong to the metric space itself. The definition is equivalent to

d (x_{n}, x) \to 0

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