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A new construction of the real numbers

Published online by Cambridge University Press:  03 November 2016

P. Shiu
P. Shiu*
Affiliation:
Department of Mathematics, University of Technology, Loughborough, Leics. LE11 3TU
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Extract

There are two well known constructions of the real numbers from the rationals—namely the Dedekind cuts method in which a real number is defined as a class of rationals, and the Cantor–Cauchy completion method in which a real number is defined as an equivalence class of Cauchy sequences of rational numbers. In this article we give a new construction of the reals from the rationals in which a real number is defined as an equivalence class of sets of natural numbers.

Type
Research Article
Information
The Mathematical Gazette , Volume 58 , Issue 403 , March 1974 , pp. 39 - 46
Copyright
Copyright © Mathematical Association 1974

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