One must not forget the reason for tolerant comparisons. It is to allow
for the fact that many rational numbers are not representable in a
binary numbering system. The FORTRAN example of 1=3*1/3 is false
(remember, / in FORTRAN is division, not reduction) is also not
intuitive. APL and J have redefined equal to mean approximately equal
unless fuzz is set to zero. To me that seems to fit the real world
better than defining equal to mean exactly equal.
I have listened to many science segments on PBS by a University of
Houston Physics professor. He made a segment on what is "dry". He was
simply saying that the definition depends on its context. A dry dish
from the dish washer is considered dry for household use but a chemist
would not consider it dry unless it spent hours in an autoclave. And
I'm sure that there are some situations where that would not be
considered "dry".
And don't forget a famous attorney who also happened to be president of
the United States who said, "It depends on what the definition of 'is' is."
Miller, Raul D wrote:
Sylvain Baron wrote:
In 1902, in a book called "Science and Hypothesis" Henri Poincare
wrote about physical and mathematical continuum :
" We cannot believe that two quantities which are equal to a third are
not
" equal to one another
Is this an axiom?
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