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Date: Tue, 03 Nov 1998 9:05 -0600Correct. Loosely, complex numbers lose the ordering, quaternions lose
From: "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 seem to recall that there are only a finite set algebras 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?