CharlesB at SPAMCNCL.ci.detroit.mi.us
Fri Apr 20 12:16:57 MDT 2001
Who invented "inverse" and "reciprocal ? Didn't arithmetic come about before the
theory explaining it with inverses and reciprocals ?
>>> schaffer at optonline.net 04/20/01 02:02PM >>>
> For someone who is starting out in arithmetic, they can add zero,
> subtract zero,
zero is the identity element in addition operation: n + 0 =
n. subtraction is the inverse operation to give the identity, so -n is
defined at the inverse of n such that -n + n = 0.
> multiply by zero, but not divide by zero.
in the same way, multiplication has an identity element, mulitply by
_1_, that is 1*n = n. division then gives the inverse for
multiplication, and you get the reciprocals, as i outlined earlier.
so, zero is not the identity element in the algebra of multiplication
of numbers. multiply by zero is well defined but stands by itself.
> I understood someone to be saying paradoxes aren't really very
> significant in mathematics and its development.
i'll leave this for another time.
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