#### Posers and Puzzles

1. 08 Nov '04 19:13
For you math people out here: someone told me the following suspicion:

There exists an overcountable subset of R that isn't dense in R.
(overcountable: not isomorphic/no bijection with N; dense: every interval* around every element (I do not mean &quot;all elements&quot; here) of the set includes more elements from that set)

I have the idea that it isn't true, because Q is countable and already dense in R. Can anyone shed some light on this?

*: I'm not sure this is the correct word, but you get the idea: (a,b) \subset R with a,b \in R, a&lt;b.
2.  Acolyte