Find a metric space and a closed, bounded subset in it which is not compact.
The Attempt at a Solution
I know that a metric space is a space that has definition such that a point has a distance to any other point. However, I know a compact space is bounded. I'm confused on what kind of subset of a metric space could be bounded yet not compact.
Background - I'm taking this course to fill a math minor, so my knowledge of abstract concepts is limited.