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Real-valued function


In mathematics, a real-valued function or real function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain.

Many important function spaces are defined to consist of real functions.

Let X be an arbitrary set. Let denote the set of all functions from X to real numbers R. Because R is a field, may be turned into a vector space and a commutative algebra over reals by adding the appropriate structure:


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