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November 27, 2020 19:57
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paper = open("turing_paper_1936.txt", "rt") | |
for line in paper: | |
print(line[:-1]) | |
paper.close() |
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ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM | |
By A. M. TURING. | |
[Received 28 May, 1936.—Read 12 November, 1936.] | |
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 com- putable numbers. According to my definition, a number is computable if | |
its decimal can be written down by a machine. |
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