Infinity is a puzzling concept. Mathematicians say there are as many odd numbers as there are numbers altogether. That seems like saying there are as many men as there are people altogether – which we know is untrue. And if you subtract infinity from infinity, you are still left with infinity – but which infinity? Some infinities are larger than others – how can this be? John and Ken unravel the paradoxes of infinity with Rudy Rucker, Professor Emeritus of Computer Science at San Jose State University and author of Infinity and the Mind: The Science and Philosophy of the Infinite.