If C is an infinite set and B is a finite set then C\B is an infinite set. C\B means the complement of B relative to C Ok so I was thinking of doing this by contradiction. I have Assume C\B is a finite set. Then there exist a function[itex]\alpha[/itex] that is bijective from C\B to Nk for some k. Now this is were im stuck. Obviously if you have something that is infinite and you take away some finite number of thigs is still going to be infinte but how do you write that mathmatically?