### The Set of Real Functions are Countable in Applied Mathematics, Algebra of the Functions and Their Classification

Because the functions must be computable, that is, there must be a method for computing them, the set of real functions is countable. However, the number of algorithms may be counted. Uncomputable functions are useless in applied mathematics; they don’t exist. The set of countable real numbers is also a set of computable real numbers.…

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