### Qual exam problem

Posted:

**Tue Dec 18, 2012 4:38 am**How to prove that the set of real numbers can be written as the union of uncountably many pairwise disjoint subsets, each of which is uncountable?

The problem is taken from http://www.math.ucla.edu/grad/handbook/hbquals.shtml.

The problem is taken from http://www.math.ucla.edu/grad/handbook/hbquals.shtml.