```Date: Dec 2, 2012 9:58 PM
Author: Jonathan Crabtree
Subject: Re: Some important demonstrations on negative numbers

> >I have also provided a precise verbal mapping of the> instructions that reveal the logic of why the> products of both -ve x - and - x -ve are positive.> > Perhaps you can rationalize it - you can't prove it> in the mathematical sense without making prior> assumptions.Hi JoeJust letting you know I use the same verbal logic as John Wallis, credited as the inventor of the number line. QUOTEEven the rule of signs was but a consequence of "the true notion of (arithmetic] Multiplication [which] is ... to put the Multiplicand, or thing Multiplied (whatever it be) so often, as are the Units in the Multiplier." >From the latter definition Wallis argued consecutively that a) multiplication of a negative multiplicand and positive multiplier involved no more than taking the multiplicand the specified number of times, and thus getting a negative sum; b) multiplication of a positive multiplicand and a negative multiplier involved nothing more than taking the multiplicand away the specified number of times; and, finally, c) multiplication of a negative multiplicand and a negative multiplier involved "taking away a Defect or Negative," which "is the same as to supply it" ? and thus getting a positive." NOTE: My lettering for clarity.SOURCE: Symbols, Impossible Numbers, and Geometric Entanglements. by Helena M. Pycior
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