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[MUSIC]. 

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cut. 
[MUSIC]. 

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Wrong class. 
This is games without chance. 

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Tom Morley. 
this is week seven. 

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Where do we go from here? 
Our first little piece is infinite and 

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loopy games. 
Now previously we looked at hack and bush 

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games. 
And if they were red blue they were 

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mostly numbers. 
And if they had green stalks in them. 

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They were these weird mean things and 
the. 

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aton, and all kinds of good stuff. 
Now you can actually do infinite numbers 

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in this same way take a hack and bush all 
blue, all the way up, and keep on going 

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forever. 
And that's the number which 

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mathematicians call omega. 
Now, that's infinity, but there's one 

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more, one larger than that, then we take 
an infinite stalk. 

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That's, goes up like this. 
The stocks are getting shorter and 

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shorter but there's still infinitely many 
of them and they keep going on like that. 

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And then put another blue stock on top of 
them and that's omega plus one. 

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And you can take infinite stock getting 
smaller and smaller, and smaller but 

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still infinite, keep on going forever. 
And put another infinite stalk on top of 

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it. 
Keep on going forever and another 

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infinite stalk. 
Keep on going forever and that's three 

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omega. 
And you can look at omega, omega and 

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omega, omega, omega. 
And you can get larger and larger and 

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larger. 
All of these these are what mathmaticians 

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call ordinal numbers but these together 
with real numbers stood inside a number 

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system called the surreal numbers. 
Which was includes the numbers that we 

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talked about in games. 
The infinite numbers, and if you want to 

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know more about this, there's a famous 
book by Donald Knuth called Surreal 

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Numbers. 
And that's what I want to say about 

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infinite games and loopy games. 
Take care.