- 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.
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 D be a subset of
A function
is sequentially computable if, for every n-tuplet
of computable sequences of real numbers such that
the sequence
is also computable.
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Categories:- Computable analysis
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