Re: apples and oranges

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

  >  Before the introduction of imaginary numbers it was a property of the
> operation "square" that the square of any number was positive.  The
> extension to imaginary numbers abandons this property and proposes
> defining NEW entities whose square is negative.

> So too, here it is proposed to define NEW entities whose absolute value
> is negative.

> abs(Q) + abs(1) = 0 is no more perverse than i^2 +1^2 = 0

> Whether this leads to anything useful is another question, but it is
> conceptually feasible.


I'm out of my mathematical depth with my next comments and hope a more
knowledgible person will chime in to correct any gross inaccuracies that I
may make:

I seem to recall that there are only a finite set algebra's for numbers,
which is why we have real numbers, (obeying one algebra); complex numbers,
obeying the property listed above; quarternions and Octonians, which have
properties I've forgotten.  And no more?  If this statement is accurate then
it is quite likely that abs(Q) + abs(1) == 0 leads to nothing useful
(unless, it already is part of the quarternion or octonian properties.

in the above, I mean the symbol == to mean "defined to be"

Joel Rauber
rauberj@mg.sdstate.edu