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 [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
