A total function for which there is an effective method of computing its output, for every input.

A computable function can also be defined as one that can be computed by an algorithm, or (equivalently), by a Turing Machine. For example:

f(n) = n + 1 is a computable function. The algorithm that solves it takes the input and adds one. (How simple is that?)

Turing's Halting Problem is an incomputable function.

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