The Importance of Infinity

Richard Martin: Some infinities are bigger than others, naively, infinity is just infinity. They're all equally infinite, but they're not. Some you can't put in one to one correspondence with the others. And lastly, Patrick, could you explain the diagonal argument made by Deutsch in chapter 15, the beginning of infinity? Why is the hotel never full? I do go through precisely the argument in my video on a window into infinity. Merry Christmas, Richard Martin.