On Fri, 22 Jul 2005, Chris McCormick wrote:
In both mathematics and computing, a modulus is calculated from the remainder of the division. Nobody "could've picked" anything.
In mathematics, modulo is a way to reduce an algebraic structure into a smaller such structure. For example, if you quotient a Ring by an Ideal of that Ring, it gives you a modulo Ring. e.g. Z/16Z is the set of equivalence classes in which its zero is really the Ideal 16Z, that is, {0,16,-16,32,-32,etc}. The other elements are the Cosets of that Ideal. A "canonical projection" function takes each element of Z making it correspond to the element of the modulo Ring that contains it. If you try inverting that function, you will have to choose a representant of each set so that the inverse becomes 1-to-1. This is why I am talking about picking.
http://mathworld.wolfram.com/Congruence.html http://mathworld.wolfram.com/QuotientRing.html
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