Re: Division by zero

Nicolas.Capens@xxxxxxxxx wrote:
Hi all,

I have a theory to work with division by zero, and it might have some
use in computer science.

I got inspired by Dr. Anderson's 'nullity' number:
http://www.bookofparagon.com/News/News_00012.htm. But as far as I know
it doesn't solve any real problem. At the best he proves that by
allowing a nullity number off the real number line, 0^0 = 0 / 0, in
other words NaN = NaN unlike IEEE 754. I don't think that really helps
us. My proposal does solve actual division by zero problems.
....
One problem is that addition of numbers with different Q exponent can't
be defined in a useful way. Powers and roots are definable, but then
the Q exponents are no longer integers. For example the square root of
-4 / 0 is 2*i*Q^-0.5. This illustrates that i and Q are orthogonal,
thus defining a three-dimensional space. In this space 0^0 is still
undefined though.

Any thoughts about this?
....

If I remember correctly, the NaN and Infinity treatment in IEEE754 was
inspired not just by theory, but by real algorithms that had simpler,
more efficient representations with the extended numbers.

In the same spirit, can you identify some algorithms that would be
simplified by your Q numbers, given the restrictions?

Patricia
.

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