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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.