Either we define discontinuous functions or multivalued functions.
2.
But on top of that, you want pointwise convergence to a discontinuous function.
3.
BBO can therefore be used on discontinuous functions.
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As well as introducing discontinuous functions, as we discussed above, he conceived the calculus as operational symbols.
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An even more general result is the Carath�odory existence theorem, which proves existence for some discontinuous functions ?.
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If the law of the excluded middle held, then this would be a fully defined, discontinuous function.
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It extends the classical finite element method by enriching the solution space for solutions to differential equations with discontinuous functions.
8.
The construction of discontinuous functions fails because a function is identified with a curve, and the curve cannot be constructed pointwise.
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Arbogast won the prize with his essay and his notion of discontinuous function became important in Cauchy's more rigorous approach to analysis.
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It extends the classical finite element method ( FEM ) approach by enriching the solution space for solutions to differential equations with discontinuous functions.
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