In paragraph 9, 10 I give some arguments with the intention of showing that the computable numbers include all numbers which cuold be naturally be regarded as computable. In particular, 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, the numbers ¼, e, 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 so great, and in many ways similar to the class of real numbers, it is nevertheless enumerable. In paragraph 8 I examine certain arguments which would seem to prove the contrary. By the correct application of one of these arguments, conclusions are reached which are superficially similar to those of Gödel. [...]
