Calculus; paradoxes in mathematics

Charles Brown CharlesB at CNCL.ci.detroit.mi.us
Fri Apr 20 09:45:11 MDT 2001



>>> david.welch at st-edmund-hall.oxford.ac.uk 04/20/01 11:27AM >>>
On Fri, Apr 20, 2001 at 09:51:36AM -0400, Charles Brown wrote:
> Why is it that one cannot divide by zero ? Seems like special pleading.
>
The definition of integer division is that a divides b if there exists
r and q such that a = r * b + q and 0 <= q < b (In words, a equals
r multiplied by b plus q and q is greater than or equal to zero and less
than b).  If b is zero then there are no pairs of numbers that satisfy
that equation for any a, as can easily be verified.

((((((((

CB:

Who originated this definition ?  Most division is done by people who don't use it.   Didn't division of integers exist before this definition ? Still seems like special pleading, arbitrary definition. Isn't this definition introduced to avoid paradoxes of some sort ?




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