Computable real function

In mathematical logic, specifically computability theory, a function is sequentially computable if, for every computable sequence of real numbers, the sequence is also computable.

A function is effectively uniformly continuous if there exists a recursive function such that, if

then

A real function is computable if it is both sequentially computable and effectively uniformly continuous,[1]

These definitions can be generalized to functions of more than one variable or functions only defined on a subset of The generalizations of the latter two need not be restated. A suitable generalization of the first definition is:

Let be a subset of A function is sequentially computable if, for every -tuplet of computable sequences of real numbers such that

the sequence is also computable.

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References


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