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A criterion for differentiability

Published online by Cambridge University Press:  31 October 2008

A. M. Macbeath
A. M. Macbeath
Affiliation:
Queen's College, Dundee.
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There are two alternative methods of defining the concept of “convergence” of a sequence, one involving explicit mention of the limit, the other (Cauchy's condition) giving a necessary and sufficient condition in terms of the elements of the sequence only. The two definitions are equivalent, because of the property of completeness of the real number system.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 40 , January 1956 , pp. 8 - 11
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

page 9 note 1 cf. Hardy, , Littlewood and Polya, Inequalities (Cambridge, 1934), p. 34.Google Scholar