> I wasn't crazy about that line, but basically, sines and cosines make much less sense over say, the rational numbers, whereas polynomials work just fine. The

> I wasn't crazy about that line, but basically, sines and cosines make much less sense over say, the rational numbers, whereas polynomials work just fine. They're the most general "nice" function one can define over an arbitrary commutative ring. This is rather a tautology since polynomials are exactly defined this way. I can imagine that if we built a (fictional) number system rather on properties of the Fourier transformation, sines and cosines would be very natural operations that would have a deep generelization when sufficiently abstracted.