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About: Critical pair (order theory)     Goto   Sponge   NotDistinct   Permalink

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In order theory, a discipline within mathematics, a critical pair is a pair of elements in a partially ordered set that are incomparable but that could be made comparable without requiring any other changes to the partial order. Formally, let P = (S, ≤) be a partially ordered set. Then a critical pair is an ordered pair (x, y) of elements of S with the following three properties: * x and y are incomparable in P, * for every z in S, if z < x then z < y, and * for every z in S, if y < z then x < z.