A proposition...

For all x in R, there exists a sequence a_n in Q such that the limit of a_n as n->+inf = x

This seems trivially false to me just from cardinality arguments (e.g. if you assume it's true then the cardinality of Q being less than the cardinality of R immediately implies that there are two different x in R that must have the same limit in Q), but I'll be damned if I can prove it rigorously.  Is there an easier way?

>>22
Oh good, you're >>16. I've had some other idiot trying to outdo me when he obviously has no idea what he's talking about.

I think I'm taking issue with the fact that S has infinitely many elements, and yet you're trying to pick out some random two of them for no apparent reason. How do you know you're choosing the right ones? How do you know, even more importantly, that you CAN choose some two elements? It might be impossible in some pathological sets.