Virgil
Posts:
8,833
Registered:
1/6/11


Re: Uncountable?
Posted:
Apr 25, 2014 1:52 PM


In article <ad3kl9tum3fm2lb8f9fehagjb4fumm7h3a@4ax.com>, quasi <quasi@null.set> wrote:
> Virgil wrote: > >William Elliot wrote: > > > >>Let C be a collection of open subsets of R that cover Q. > >>Can S = R  \/C ever be uncountable? > > > >It cannot even be nonempty! > > > >Every open cover of Q as a subset of R covers R. > > That's not true. > > As a simple example, let > > A = (oo,sqrt(2)) > > B = (sqrt(2),oo)o]
Oops! 

