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An Informal Arithmetical Approach to Computability and Computation, III

Published online by Cambridge University Press:  20 November 2018

Z.A. Melzak
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It is assumed that the reader is acquainted with the first two parts of the present paper, [1] and [2], in which there was developed informally the theory of a certain class of hypothetical computing devices, the Q-machines. In the present part of the paper we develop a way of describing Q-programs and Q-computations; then, following the theorem in [2], we obtain some further connections between the arithmetical nature of a number x and the computational schémas for generating sequences of rational numbers converging to x; and finally, by means of the usual device of Goedel numbering we begin to examine some properties of programs which operate on programs.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 5 , December 1966 , pp. 593 - 609
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Melzak, Z.A., Canad. Math. Bull., vol. 4, no. 3, Sept. 1961, pages 279-293.Google Scholar
2. Melzak, Z.A., Canad. Math. Bull., vol. 7, no. 2, April 1964, pages 183-200.Google Scholar
3. Schneider, T., Einfuehrung in die transzendenten Zahlen. Springer, 1957.Google Scholar