| dbo:abstract |
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 . The theorem is named after Henri Poincaré, who conjectured it in 1883, and Carlo Miranda, who in 1940 showed that it is equivalent to the Brouwer fixed-point theorem. (en) |
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wiki-commons:Special:FilePath/PoincareMiranda.png?width=300 |
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right (en) |
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A graphical representation of Poincaré–Miranda theorem for (en) |
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dbc:Topology dbc:Real_analysis |
| rdfs:comment |
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 . (en) |
| rdfs:label |
Poincaré–Miranda theorem (en) |
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wikipedia-en:Poincaré–Miranda_theorem?oldid=1109450625&ns=0 |
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