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From: jacko on 14 Apr 2010 09:00
Hi

if -13/-6= 1 remainder -1 due to the number line being offset in the
negatives.

3,2,1,-1,-2,-3 etc.

A formally consistent ring is defined. let the representation be for
positive x, x-> x-1 and for negative x, x -> x. This then gives
addition as a+b+1 and subtraction as a-b-1, leaving the number in the
same representation.

To do multiply normalize any positive number by x+1 and any negative
number by -x.
Do the multiply and perform a representation mapping, after applying
the sign rule to the product.

For division, do the division, and calculate the remainder using the
field remainder operation
rem=dividend<->quotient<*>divisor.

Now x/0 is an evaporated problem. -1/-1=1 rem -1, and all positive
numbers have the correct result.

Now if you scale this number system by planks constant the extra unit
interval on the quantum or integer line could be split in two as hbar/
2

Another interesting thing to see is the monad - is simply NOT x, and
the mathematical (1-x) within the field operator set.

Now p-1 is a common expression.

Cheers jacko
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