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## Homework Statement

show that (the range of) a sequence of points in a metric space is in general not a closed set. Show that it may be a closed set.

**2. The attempt at a solution**

I don't know where to start.

For example, if we are given a sequence of real numbers and the distance between a and b is defined as |a-b|, it asks us to show that a sequence of real numbers is in general not a closed set?