On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans <char...@declaresub.com> wrote:
> >On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: > >> Jaime Fernandez del Rio <jaime.f...@gmail.com> writes: >>> I am pretty sure that a continuous sequence of >>> curves that converges to a continuous curve, will do so uniformly. >> >> I think a typical example of a curve that's continuous but not >> uniformly continuous is >> >> f(t) = sin(1/t), defined when t > 0 >> >> It is continuous at every t>0 but wiggles violently as you get closer >> to t=0. You wouldn't be able to approximate it by sampling a finite >> number of points. A sequence like >> >> g_n(t) = sin((1+1/n)/ t) for n=1,2,... >> >> obviously converges to f, but not uniformly. On a closed interval, >> any continuous function is uniformly continuous. > >Isn't (-?, ?) closed? What is your version of the definition of "closed"? >Charles Yeomans -- http://mail.python.org/mailman/listinfo/python-list