Editing Computable function (section)

==Church–Turing thesis==

{{main|Church–Turing thesis}}

The '''Church–Turing thesis''' states that any function computable from a procedure possessing the three properties listed [[#Characteristics of computable functions|above]] is a computable function. Because these three properties are not formally stated, the Church–Turing thesis cannot be proved. The following facts are often taken as evidence for the thesis:
* Many equivalent models of computation are known, and they all give the same definition of computable function (or a weaker version, in some instances).
* No stronger model of computation which is generally considered to be [[effectively calculable]] has been proposed.

The Church–Turing thesis is sometimes used in proofs to justify that a particular function is computable by giving a concrete description of a procedure for the computation. This is permitted because it is believed that all such uses of the thesis can be removed by the tedious process of writing a formal procedure for the function in some model of computation.