FOM: nowhere differentiable/natural
Martin Davis
martin at eipye.com
Thu Aug 5 18:12:51 EDT 1999
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
(Add 1 and get 0)
http://www.eipye.com
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