Date: Nov 29, 2012 1:31 AM Author: Peter Duveen Subject: Re:
Some important demonstrations on negative numbers To demonstrate
that 1/-a = -(1/a): (1/-a) x -a = 1 definition of 1/-a eq.1 - -
(1/a) x a = -1 definition of 1/a - -1 (1/a) x a = -1 (1/a) x -1
x a = -1 (1/a) x -a = -1 - -(1/a) x -a = 1 eq.2 >From eq. 1 and
eq. 2: - -(1/a) = (1/-a). Perhaps a bit clumsy, but once
demonstrated in its generality, the student no longer needs to
wonder about this relationship when he sees a negative number in
the denominator. As far as even clumsier analogies, that is fine
to interpret the result as long as the result has been
demonstrated clearly. Seems those who took geometry should
easily assimilate such a demonstration (proof) .