3
$\begingroup$

If $S$ is a bounded set of real numbers, how can we prove that there are distinct sequences in $S$ that converge to $\sup S$ and $\inf S$?

I'm not even sure how to begin on this problem. I know the set $S$ is bounded so it has a supremum and an infimum.

  • 0
    It's not clear what you mean by "distinct sequences." But if $S=\{0\}$, it's not true under the meanings I might guess you intended.2012-12-07

2 Answers 2