Alex López-Ortiz has a nice math website at Waterloo. I happened on it in checking for Euler's Theorem for Linking Constants, as I've just named the theorem I talked about on my birthday. He has interesting things to say about defining exponentiation, and Euler's Theorem. (There is not a necessary way to define the value of x^y when y is not an integer, but rather is a fraction, or negative, or imaginary.) I also like his discussion of the Erdos number, the co-authoring distance between a person and Erdos, and of the Axiom of Choice. Of most importance is his set of proofs and informal proofs (?) that 0.9999...=1. That statement is not a joke, like the proof that 1=2 that I discuss in the Introduction to Games and Information. Rather, it is true and makes sense, in the same way that 0.11111 = 1/9. The limit of .9 + .09 + .009 + ... is not .999990000, but 1. I suspect I've been sloppy in my economics writing and said things like "Is it an equilibrium for somebody to bid 0.9999... instead of 1?" where I mean "Is it an equilibrium for somebody to bid 0.9999000 instead of 1?" I'll have to keep my eye open for that kind of error.

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