FOM: nowhere differentiable/natural

[Martin Davis]

At 04:44 PM 8/5/99 +0100, Harvey Friedman wrote:
>Here is a particularly natural example of a continuous nowhere
>differentiable selfmap of the closed unit interval.
>
I believe this example suffers from the (minor) defect of possessing an
infinite derivative everywhere.

I don't see anything "unnatural" about Weierstrass's original example:
                 
             SUM[0 to infinity] [b^n cos(a^n \pi x)]

Here 0<b<1 and a is an odd positive integer. (Titchmarsh, THEORY OF
FUNCTIONS, p.351.)





                           Martin Davis
                   Visiting Scholar UC Berkeley
                     Professor Emeritus, NYU
                         martin at eipye.com
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                       http://www.eipye.com