You're mistaken. Closed does not disqualify countable. A closed set
is a set that contains all of its limit points. A countable set is
one that can be put into a 1:1 correspondence with Q.
For example, the natural numbers as a subset of the reals are closed
and countable. Countable, you won't argue with. There are no limit
points for this set, so the set is vacuously closed. Thus, we have
found a set that is closed and countable.
Gotta love advanced calc!
Joel Gluskin
Wash U Academic Team President
--- In quizbowl_at_yahoogroups.com, koszul <no_reply_at_y...> wrote:
> The answer was closed. Compact was disqualified by the second
> example of countable sets (since infinite discrete sets are not
> compact, eg the naturals as a subset of the reals). However, unless
> I'm forgetting a qualifier, countable disqualifies closed, too,
since
> the set of reciprocals of natural numbers as a subset of the reals
is
> countable but not closed. Does anyone have the text handy?
> David