Suppose you have a programming language $\mathcal L$ designed to efficiently perform calculations with real numbers. In particular, it allows for the definition of (computational, deterministic) functions which take one number as an argument and return a number:
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Let $f:\ \mathbb R \to \mathbb R$ be an arbitrary mathematical function, mapping real numbers to real numbers. What is the probability that $f$ can be modeled using a function programmed in $\mathcal L$?
Assume that $\mathcal L$ can handle real numbers in an arbitrarily large range, with infinite precision. The programmed function $F$ is of finite length.