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 primitive recursive function such that, if , then .
A real function is thus computable if it is both sequentially computable and effectively uniformly continuous.
These definitions can be generalized to functions of several variables as follows: let be a subset of . A function is sequentially computable if, for every -tuple of computable sequences of real numbers such that
for all , the sequence is also computable.
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