Talk:Smooth function

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Mathematics rating: Start Class Mid Priority  Field: Analysis

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)

[edit] moving this to differentiable function

Any objections to moving this to differentiable function? That is currently a redirect to derivative. --MarSch 30 June 2005 16:07 (UTC)

Infinitely differentiable is not the same as (one time) differentiable.--Patrick June 30, 2005 20:58 (UTC)
smooth functions are a very special case of differentiable functions, but there is no such article yet. I think it would be easy to expand this once it is moved there.--MarSch 1 July 2005 10:09 (UTC)

Differentiabillity class could also be merged there. In the intro here C^1 and all that is explained so I think it would be a natural move. --MarSch 1 July 2005 10:12 (UTC)

Yes, I think merging is good. However, differentiable function sounds like there is one type of differentiability, so perhaps differentiability or differentiability of functions or the existing name differentiability class is best.--Patrick 1 July 2005 14:38 (UTC)
There should be a separate article "Differentiability Classes" and all the stuff explained in the intro about C^1 etc should go there, since to define a smooth function you would have to define differentiability classes first; the latter are more fundamental. --Stephen 9 March 2008 16:52 British Time —Preceding unsigned comment added by 217.44.113.21 (talk) 16:53, 9 March 2008 (UTC)