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,see
{{Citation|last=Grzegorczyk|first=Andrzej|title=On the Definitions of Computable Real Continuous Functions|journal=Fundamenta Mathematicae|volume=44|year=1957|pages=61–77|url=http://matwbn.icm.edu.pl/ksiazki/fm/fm44/fm4415.pdf|format=PDF}}
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.
{{PlanetMath attribution|id=6248|title=Computable real function}}