From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 12 Nov 1999 09:53:01 -0600
Hi all-
Peter Vajk writes:
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[SIMPLE PREMISE:] IF the functional relations mentioned above are
CONTINUOUS functions,
[SIMPLE CONSEQUENCE:] THEN, over SOME finite range of values, EITHER
relationship is very nearly LINEAR. (In calculus terms, every
continuous function, over some finite domain, may be described
arbitrarily accurately in terms of its value and its first derivative at
a point inside that finite domain.)
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Sorry, Peter, but continuity does not imply differentiability.
Mathemeticians give examples of functions that are everywhere continuous (they
satisfy the axioms of continuity) and are nowhere differentiable.
Also, when material fractures, the strain is not a continuous function
of the stress.
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography