- #1
AxiomOfChoice
- 533
- 1
Consider the closed interval [tex]A = [a,b]\subset \mathbb{R}[/tex]. Are the only dense subsets of [tex]A[/tex] the set of all rational numbers in [tex]A[/tex] and the set of all irrational numbers in [tex]A[/tex]? Something tells me that there's got to be more than that, but I can't think of any examples.
Thanks in advance for your help.
Thanks in advance for your help.