Computable real function: Difference between revisions

Revision as of 17:45, 12 April 2009

Revision as of 22:25, 20 April 2009

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A [[real function]] is ''computable'' if it is both sequentially computable and effectively uniformly continuous.

These [[definition]]s can be generalized to functions of more than one [[Variable (mathematics)|variable]] or functions only defined on a [[subset]] of <math>\mathbb{R}^n.</math> The generalizations of the latter two need not be restated. A suitable generalization of the first definition is:

Let <math>D</math> be a subset of <math>\mathbb{R}^n.</math> A function <math>f \colon D \to \mathbb{R}</math> is ''sequentially computable'' if, for every <math>n</math>-tuplet <math>\left( \{ x_{i \, 1} \}_{i=1}^\infty, \ldots \{ x_{i \, n} \}_{i=1}^\infty \right)</math> of computable sequences of real numbers such that

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[[Category:Mathematical logic]]

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