Posted by
Phil Henshaw-2 on
Jul 26, 2007; 7:57pm
URL: http://friam.383.s1.nabble.com/DIFFERENTIABILITY-AND-CONTINUITY-tp524276p524296.html
Nick,
There might be several definitions of continuity, that correspond to
different properties, some included in each other and some not. My guess
is that the non-differentiable type being referred to, but not named or
described, is different from the differentiable one(s) that one more
commonly runs into, and given the complicated ways people can define things
maybe there are several kind of choices for guessing what's being talked
about. The one mentioned is not defined it seems, except by way of asking
the poor reader for a "gee whiz oh gosh" response of some sort. ...so
belaboring the point... is there something missing??
On 7/25/07, Nicholas Thompson <nickthompson at earthlink.net> wrote:
>
>
>
> 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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