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Some Solved and Unsolved Problems in the Theory of Numbers*

Published online by Cambridge University Press:  03 November 2016

R. Rado
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Extract

Broadly speaking, the development of mathematical thought has proceeded along two main channels. On the one hand mathematicians have been studying properties of objects which in some obvious and intuitive sense form what is called a continuum, while others were concerned with objects which one conceived as being discrete and well separated from each other. An example of the former type of mathematics is the differential calculus; and the theory of the distribution of the prime numbers 2, 3, 5, 7, 11, … belongs to the mathematics of the discrete. The mysteries of the epsilontic—so dear to us all: “If epsilon is sufficiently small, then delta will be as small as we please”—have no direct counterpart in the theory of the natural numbers 1, 2, 3, …. The underlying idea of the continuum seems to be that of motion, while the discrete and separable appears to be more of a static nature.

Type
Research Article
Information
The Mathematical Gazette , Volume 25 , Issue 264 , May 1941 , pp. 72 - 77
Copyright
Copyright © Mathematical Association 1941

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Footnotes

*

A paper read to the Sheffield Branch of the Mathematical Association.

References

* A paper read to the Sheffield Branch of the Mathematical Association.