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Hi Bob-Physics
In response to:
*********************************************************
Hi Jack,
Out of curiosity, can you indicate any mathematical statements in
where " = " does not mean a numerical (or perhaps vector or tensor)between
equality?
************************
At the risk of flagellating a moribund equine, yes:
VxB = |V||B|sine(theta) where "theta" is the angle
the two vectors V and B.cross
This statement is a mathematical identity (definition of the
product) and has no physical content.the
Contrast that use of the equal sign with:
F = VxB
which does have physical content. It relates the numerical values of
6 independently measurable components of V and B with the threeindependently
measurable values of the components of F.second
The equal sign in the first equation stands for "is", in the
equation it predicts the result of an experiment.
John expanded on this theme in his post following your question.
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