Now on ScienceBlogs: Charles Darwin February 12, 1809 - April 19, 1882
Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it.
Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems.
Category: 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...
Posted by Mark C. Chu-Carroll at 5:15 PM • 11 Comments •
Category: Surreal Numbers
(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...
Posted by Mark C. Chu-Carroll at 9:42 PM • 10 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 9:29 PM • 2 Comments •
Category: Surreal Numbers
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:...
Posted by Mark C. Chu-Carroll at 10:00 PM • 1 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 9:23 PM • •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 8:05 AM • 5 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 8:05 AM • 17 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 10:09 PM • 14 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 9:54 PM • 4 Comments •
Category: Surreal Numbers
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...
Posted by Mark C. Chu-Carroll at 9:16 PM • 6 Comments •
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