Posted by
Frank Wimberly on
Jul 26, 2007; 8:59pm
URL: http://friam.383.s1.nabble.com/DIFFERENTIABILITY-AND-CONTINUITY-tp524276p524297.html
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???????????wimberly3 at earthlink.net
-----Original Message-----
From:
[hidden email] [mailto:
[hidden email]] 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
>
>
============================================================
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