Re: rational - irrational question

"William Elliot" > 
> Thus you're left pondering the question if there's an uncountable
> set of reals whose closure is disjoint from the rationals, Q.
> 
> That is an interesting question.  A weaker interesting question is:
> does an uncountable set of reals have uncountably many limit points?
> 
> According to my notes, such a set has uncountably many limit
> points in the set itself.  The other question I have no answer.


It's been 40 years since I took topology, but that sounds right.

And it means there is no uncountable set of slopes and radii 
such as I've been looking for. 

(But I think I've proved that there is for the countable case 
(in another post).)

Thak's again.