The set of integers is smaller than the set of real numbers. This I understand through logic. I've also heard that the set of irrationals is larger than the set of rationals. How is this so? And so I'm guessing the set of reals is larger than both the set of rationals and irrationals since it's both those sets combined. Here's where I'm even more confused. I've heard that the set of complex numbers is the same size as the set of real numbers. Now logic kicks in again and tells me that for every real number there are infinite complex numbers to go with it. So in a sense, whatever sized infinite the set of real numbers is, the complex numbers should be this size squared. This can be seen geometrically as well.