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About: Poincaré–Miranda theorem     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the Poincaré–Miranda theorem is a generalization of the intermediate value theorem, from a single function in a single dimension, to n functions in n dimensions. It says as follows: Consider continuous functions of variables, . Assume that for each variable , the function is constantly nonpositive when and constantly nonnegative when . Then there is a point in the -dimensional cube in which all functions are simultaneously equal to .