RE: Calculus

["Craven, Jim" <jcraven@xxxxxxxxxxxxx>]

On a parenthetical note, The Mayans developed and used the concept of 0 some
600 years before it was "discovered" in Europe. For some interesting
expositions on some of the "undiscovered" origins of central concepts in
advanced mathematics see "Native American Mathematics" Ed by Michael P.
Closs, University of Texas Press, Austin, 1986. Since Calculus is
essentially the mathematics of change and non-linearity, Indigenous
paradigms focusing on the essential changability and non-linear integration
of aspects of a totality, seen as a totality of interrelated aspects, the
essential concepts and operations of calculus were known and practiced by
some Indigenous societies long before "credit" was given for the same
"discoveries" elsewhere.

Jim C.




-----Original Message-----
From: Charles Brown [mailto:CharlesB@xxxxxxxxxxxxxxxxxxxxx]
Sent: Friday, April 20, 2001 11:29 AM
To: marxism@xxxxxxxxxxxxxxx
Subject: Re: Calculus


Who invented "inverse" and "reciprocal ?  Didn't arithmetic come about
before the theory explaining it with inverses and reciprocals ?

CB

>>> schaffer@xxxxxxxxxxxxx 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.