I've had a discussion with two friends about infinity. I am of the opinion that infinities come in different sizes and some infinities can be bigger than others. My argument goes somewhat like this: Between the numbers 1 and 2 there are infinite real numbers. Between 1 and infinity there are infinite integers. However, since for any two successive integers there is an infinite number of real numbers, there are more real numbers than integers. Despite my best efforts, neither agree with me. They say that infinity is infinite and since "it goes on forever nothing can be greater than it." But I think this definition is somewhat prosaic and has limited mathematical value. What do you think? Can infinities be of different sizes?