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Continuity and Irrational Number

Published online by Cambridge University Press:  03 November 2016

G.J Whitrow
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Extract

In a previous article I have outlined my conception of the rôle of history in the exposition of mathematical technique. In this article I attempt to provide my bare thesis with a respectable clothing of practicability The treatment of Number and Continuity which follows is a short and very sketchy historical supplement to the technical treatment of the same subjects in, say, the earlier chapters of Hardy’s Pure Mathematics.

Type
Research Article
Information
The Mathematical Gazette , Volume 17 , Issue 224 , July 1933 , pp. 151 - 157
Copyright
Copyright © The Mathematical Association 1933

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References

Page 151 of note * “The Importance of the History of Mathematics in relation to the Study of Mathematical Technique”, Math. Gazette, XVI (October 1932), p. 225.

Page 153 of note * My diagram illustrates what this sentence means. A comes between C n and thus C n+1 on CC 1 C 2. and thus the constructed diagonal “falls short of” or “goes beyond” A.

N.B.—To the Pythagoreans the “strips” C 1 C 2, etc.. and not the partitions C 1, C 2, etc., were the “points” of the diagonal.

Page 154 of note * Eudoxus and Archimedes are, in a sense, parallel to Newton and Gauss, respectively.