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: I'm sort of ashamed that I didn't know that there was a Fundamental Theorem of Arithmetic. This makes many things clearer, including why 1 is not considered a prime number (as I suspected from various hemming-and-hawing explanations I've gotten over the years, there's no real reason--it just makes the FTA a lot uglier).

However, this revelation increases my forboding feeling that algebra is in some bizarre sense the derivative of calculus, and arithmetic the second derivative.

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