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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.
Dr. Tom MorleyProfessor
