DIFFERENTIABILITY AND CONTINUITY

Posted by Nick Thompson on Jul 25, 2007; 6:09pm
URL: http://friam.383.s1.nabble.com/DIFFERENTIABILITY-AND-CONTINUITY-tp524276.html



Deep down in the tangle of >>>>>'s I just found this gem.  The record is
two confused for me to know who to thank so I will thank you ALL.

> What you have given is the "handwaving" version of the proof. The
> trouble is that human imagination can easily get us into trouble when
> dealing with infinities, which is necessarily involved in dealing with
> the concept of continuity. In the above example, you mention that
> continuity is important, but say nothing about differentiability. Are
> you aware that continuous curves that are nowhere differentiable
> exist? I fact most continuous curves are not differentiable. By most,
> I mean infinitely more continuous curves are not differentiable than
> those that are, a concept handled by "sets of measure zero".

OK.  I AM BEING CALLED TO A MEAL AND YOU ALL KNOW WHAT HAPPENS WHEN ONE
DOESNT ANSWER THAT CALL.  BAD KARMA

AM I WRONG THAT BOTH CONTINUITY AND DIFFERENTIABILTY OF AT LEAST THE
primary FUNCTION ARE A PREMISE OF THE MEAN VALUE THEOREM.  

MORE TO THE POINT,  ARE YOU ALL CONVERGING AROUND THE ASSERTION THAT THE
MEAN VALUE THEOREM CANNOT BE DONE WITH OUT ALGEBRA?  AS OPPOSED THE THE
VIEW I WAS ENTERTAINING THAT THE MEAN VALUE THEORY IS A LOGICAL PROOF THAT
IS REPRESENTED ALGEBRAICALLY FOR PEDIGOGICAL PURPOSES.  

SORRY TO TWIST EVERYBODY'S KNICKERS ABOUT THIS.  BUT IRRITATING AS IT MAY
BE TO YOU ALL, THIS CONVERSATION HAS BEEN VERY HELPFUL TO ME.  

NICK

nick
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