If C is countable, then |N|=|C|, so there exists a bijection bewteen N and C, but does this imply that |R\N| = |R\C|? It is intutively believable, but I don't see how it rigorously follows. What is the bijection between R\N and R\C? Is it provable in general that If |A|=|C| and |B|=|D|, then |A\B| = |C\D| ? If so, how can we formally prove this? i.e. how to define the bijection? Thanks!