Well, according to any conventional definitions differentiability implies continuity.
--- Frank C. Wimberly 140 Calle Ojo Feliz (505) 995-8715 or (505) 670-9918 (cell) Santa Fe, NM 87505 [EMAIL PROTECTED] -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Phil Henshaw Sent: Thursday, July 26, 2007 8:29 PM To: 'The Friday Morning Applied Complexity Coffee Group' Subject: Re: [FRIAM] DIFFERENTIABILITY AND CONTINUITY Yes, I thought that might be the type, though I think there are also others. Allowing 'continuous' as a general term to include curves that freely include discontinuities of direction redefines the term in most people's minds, and is the reason for the 'surprise' that it doesn't have the usual properties. Ther's a couple other interesting classes of continuities worth exploring, the impose constraints on the, as well as make the analysis complicated. One is the class of continuous curves that are consistent with energy conservation (they can't have infinite derivatives). Another is the class of curves formed by having a rule for finding point betweem any two, but having no formula. The latter is interesting because it's everywhere discontinuous, but fairly easy to make differentiable... :-) Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844 e-mail: [EMAIL PROTECTED] explorations: www.synapse9.com > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Frank Wimberly > Sent: Thursday, July 26, 2007 4:59 PM > To: 'The Friday Morning Applied Complexity Coffee Group' > Subject: Re: [FRIAM] DIFFERENTIABILITY AND CONTINUITY > > > See for example: > > http://www.math.tamu.edu/~tvogel/gallery/node7.html > > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz (505) 995-8715 or (505) > 670-9918 (cell) Santa Fe, NM 87505 [EMAIL PROTECTED] -----Original > Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Phil Henshaw > Sent: Thursday, July 26, 2007 1:58 PM > To: [EMAIL PROTECTED]; 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 <[EMAIL PROTECTED]> 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 > > > > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
