According this problem/solution set from an MIT class (http://ocw.mit.edu/courses/mathematics/18-100c-analysis-i-spring-2006/exams/exam1_sol.pdf), the assertion:
"Every collection of disjoint intervals in R is countable."
is True, because "every interval contains a rational number", and the rationals are countable.
It seems to me this should be False, with possible counterexample:
{ [x,x] | x is an element of R}
ie the set of all singelton intervals on R. Why isn't this a valid counterexample?