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Comparison of algebraically described sets

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I have been pondering this problem for a day or two and I have a number of ideas but a few things have tripped me up (most of all that the use of integers). The problem that I am trying to solve is how to take a number of sets and predict the results of the comparison operators on their values. For example if there where the sets A [0,1] and B [0,1,2] then the answer would be true for A == B, and "true or false" for A > B . However the trick is that the sets are described algebraically, for example one could have the sets: A: [0-5] B: A*2 ( [0,2,4,6,8,10] ) C: A*4+1 ( [1,5,9,13,17,21] ) Where here B==C is always false, but B>C and C>B are "true or false" because the ranges overlap. Simply calculating the entire sets is infeasible because they could be quite large (billions of numbers included), and so a solution involving algebraic description and ranges of some sort seem in order. The problem is made more complex than it might be because of the fact that this is dealing with integers, and so there are cases that would not exist with real numbers. Thanks, ~SPH

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