Ok, one more. You can’t leave the party without meeting Otto. He’s an infinite cat. That’s it! Thanks for coming, be it in person or virtually, and most especially, thank you for reading, commenting, and helping ScienceBlogs reach 1,000,000 comments!
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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 and infinitessimal numbers a natural part of the number system in such an
"As an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree." -Hugh Everett
One of the strangest, and yet one of the most important ideas that grew out of set theory is the idea of cardinality, and the cardinal numbers.
I've talked about the idea of the size of a set; and I've talked about the well-ordering theorem, that there's a well-ordering (or total ordering) definable for any set, including infinite ones.
Love cats! The Infinite Cat website is awesome!