Charles Brown CharlesB at
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 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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