Surreal Numbers:
So, today we're going to play a bit more with nimbers - in particular, we're going to take the basic nimbers and operations over nimbers that we defined last time, and take a look at their formal properties. This...
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Posted on May 3, 2007 5:15 PM • 11 Comments •
(A substantial part of this post was rewritten since it was first posted. I managed to mangle things while editing, and the result was not particularly comprehensible: for example, in the original version of the post, I managed to delete...
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Posted on April 30, 2007 9:42 PM • 9 Comments •
Finally, as I promised a while ago, it's time to look at the sign-expanded forms of infinites in the surreal numbers. Once you've gotten past the normal forms of surreal numbers, it's pretty easy to translate them to sign-expanded...
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Posted on April 23, 2007 9:29 PM • 2 Comments •
When I left off yesterday, we'd reached the point of being able to write normal forms of surreal numbers there the normal form consisted of a finite number of terms. But typically of surreal numbers. that's not good enough:...
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Posted on April 12, 2007 10:00 PM • 0 Comments •
On the way to figuring out how to do sign-expanded forms of infinite and infinitesimal numbers, we need to look at yet another way of writing surreals that have infinite or infinitesimal parts. This new notation is called the...
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Posted on April 11, 2007 9:23 PM • 0 Comments •
When I first read about the sign-expanded form of the surreal numbers, my first thought was "cool, but what about infinity?" After all, one of the amazing things about the surreal numbers is the way that they make infinite...
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Posted on April 10, 2007 8:05 AM • 5 Comments •
In addition to the classic {L|R} version of the surreal numbers, you can also describe surreals using something called a sign expansion, where they're written as a sequence of "+"s and "-"s - a sort of binary representation of...
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Posted on April 9, 2007 8:05 AM • 17 Comments •
The Surreal Reals I was reading Conway's Book, book on the train this morning, and found something I'd heard people talk about, but that I'd never had time to read or consider in detail. You can use a constrained subset...
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Posted on April 5, 2007 10:09 PM • 13 Comments •
Coming back from games to numbers, I promised earlier that I would define division. Division in surreal numbers is, unfortunately, ugly. We start with a simple, basic identity: if a=b×c, and a is not zero, then c=a×(1/b). So if...
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Posted on April 4, 2007 9:54 PM • 2 Comments •
Late last summer, shortly after moving to ScienceBlogs, I wrote a couple of posts about Surreal numbers. I've always meant to write more about them. but never got around to it. But Conway's book actually makes pretty decent train...
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Posted on March 29, 2007 9:16 PM • 6 Comments •
