# Prove that the closure of a bounded set is bounded.

dustbin

## Homework Statement

Prove that if S is a bounded subset of ℝ^n, then the closure of S is bounded.

## Homework Equations

Definitions of bounded, closure, open balls, etc.

## The Attempt at a Solution

See attached pdf.

#### Attachments

• Problem.pdf
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clamtrox
That looks OK to me apart from a couple of typos.

There is an easier way to prove this too though. Do you know that the closure of S is the intersection of all closed subsets containing S?

dustbin
Thanks for your input! We have not proved that the closure of S is the intersection of all closed subsets containing S... so I cannot use this result without proof.