hmm... and not all countable sets are closed either (look at the set {1, 1/2, 1/3, ..., 1/n, ...}) william On Tue, 11 Feb 2003, jagluski wrote: > 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 > > > To unsubscribe from this group, send an email to: > quizbowl-unsubscribe_at_yahoogroups.com > > > > Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service. >
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