http://friam.383.s1.nabble.com/DIFFERENTIABILITY-AND-CONTINUITY-tp524276p524300.html
others. Allowing 'continuous' as a general term to include curves that
have the usual properties. Ther's a couple other interesting classes of
make the analysis complicated. One is the class of continuous curves
derivatives). Another is the class of curves formed by having a rule
for finding point betweem any two, but having no formula. The latter
make differentiable... :-)
680 Ft. Washington Ave
> From: friam-bounces at redfish.com
> [mailto:friam-bounces at redfish.com] On Behalf Of Phil Henshaw
> Sent: Thursday, July 26, 2007 1:58 PM
> To: nickthompson at earthlink.net; The Friday Morning Applied
> Complexity Coffee Group
> Subject: Re: [FRIAM] DIFFERENTIABILITY AND CONTINUITY
>
> 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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> Meets Fridays 9a-11:30 at cafe at St. John's College
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