Um was geht es in Alan Turings Werk "On computable numbers, with an application to the Entscheidungsproblem"?

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Turing selbst sagt es zu Beginn seines Papiers:

According to my definition, a number is computableif its decimal can be written down by a machine. ...

I show that certain large classes of numbers are computable. They include, for instance, the real parts of all algebraic numbers, the real parts of the zeros of the Bessel functions, etc. 

The computable numbers do not, however, include all definable numbers, and an example is given of a definable number which is not computable.

Although the class of computable numbers is large, and in many ways similar to the class of real numbers, it is nevertheless enumerable. .

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