authors A. M. TURING
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date 5/28/1936
// [Received 28 May, 1936.—Read 12 November, 1936.]

title ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM

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Source
 https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf

The "computable" numbers may be described briefly as the real
numbers whose expressions as a decimal are calculable by finite means.
Although the subject of this paper is ostensibly the computable numbers.
it is almost equally easy to define and investigate computable functions
of an integral variable or a real or computable variable, computable
predicates, and so forth. The fundamental problems involved are,
however, the same in each case, and I have chosen the computable numbers
for explicit treatment as involving the least cumbrous technique. I hope
shortly to give an account of the relations of the computable numbers,
functions, and so forth to one another. This will include a development
of the theory of functions of a real variable expressed in terms of computable numbers. According to my definition, a number is computable
if its decimal can be written down by a machine.