[MUSIC]. cut. [MUSIC]. Wrong class. This is games without chance. Tom Morley. this is week seven. Where do we go from here? Our first little piece is infinite and loopy games. Now previously we looked at hack and bush games. And if they were red blue they were mostly numbers. And if they had green stalks in them. They were these weird mean things and the. aton, and all kinds of good stuff. Now you can actually do infinite numbers in this same way take a hack and bush all blue, all the way up, and keep on going forever. And that's the number which mathematicians call omega. Now, that's infinity, but there's one more, one larger than that, then we take an infinite stalk. That's, goes up like this. The stocks are getting shorter and shorter but there's still infinitely many of them and they keep going on like that. And then put another blue stock on top of them and that's omega plus one. And you can take infinite stock getting smaller and smaller, and smaller but still infinite, keep on going forever. And put another infinite stalk on top of it. Keep on going forever and another infinite stalk. Keep on going forever and that's three omega. And you can look at omega, omega and omega, omega, omega. And you can get larger and larger and larger. All of these these are what mathmaticians call ordinal numbers but these together with real numbers stood inside a number system called the surreal numbers. Which was includes the numbers that we talked about in games. The infinite numbers, and if you want to know more about this, there's a famous book by Donald Knuth called Surreal Numbers. And that's what I want to say about infinite games and loopy games. Take care.
