- #1
jdinatale
- 155
- 0
Ok, I don't think I'm on the right track here. I ASSUMED that the set of all countable collections [itex]\{I_k\}_{k = 1}^\infty[/itex] of nonempty open, bounded intervals such that [itex]E \subseteq \bigcup_{k = 1}^\infty I_k[/itex] is a countable set itself, which it probably isn't.
I'm not even sure where to start on this problem. I feel like I need to use the assumption that E is bounded. I know if E is bounded, then E can be covered by a finite number of nonempty open, bounded intervals.