Talk: Smooth function

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Can you quantify or make mathematically precise what you mean by a "large gap"? Phys 15:48, 2 Dec 2003 (UTC)

I believe there are a number of mathematical analysis ways. If Taylor's theorem is breaking down as an infinite series expansion, something in the remainder term is blowing up. Smooth says the Fourier transfrom drops off at infinity faster than any polynomial - one can ask for more than that. I'm pretty sure there are classes of functions between smooth and analytic that have been studied, as whole scales (are they called quasi-analytic?). Obviously it's very striking how different the zero sets are, since any closed set can be the zero set of a smooth function.

Charles Matthews 17:14, 2 Dec 2003 (UTC)

Seems protecting the semi-open intervals from interference from Wiki-syntax busibodies also damages the format.

Charles Matthews 10:09, 13 Nov 2004 (UTC)