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Lectures on the Theory of Functions of Real Variables. By James Pierpont, Professor of Mathematics in Yale University. Volume I., xii + 560 pages. (Ginn & Co., Boston, [1905].)

Published online by Cambridge University Press:  03 November 2016

Philip E. B. Jourdain
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Type
Review
Information
The Mathematical Gazette , Volume 3 , Issue 57 , May 1906 , pp. 313 - 316
Copyright
Copyright © Mathematical Association 1906

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References

page 314 note * It succeeded in making this thesis plausible.

page 314 note † Pages 46 and 48 of Fischer’s German translation (1862) of Briot and Bouquet. Cf. pp. 47-48, 49 for a slight description of the (“essential,” in Weierstraseian terms) singularity of at z=0.

page 314 note ‡ The same probably applies to Méray’s theory, since Méray was, like Weierstrass, occupied with analytic functions.

page 315 note * Cauchy’s definition of an irrational as a limit of rationals might be criticised when dealing with irrationals and the existence of limits.

Another suggestion I should like to make is that the author should illustrate that an always finite function need not be limited.

page 315 note † Cf. Russell’s, Principles of Mathematics, Vol. I., 1903, p. 327 Google Scholar note. ‘Every’ is often used for ‘any’ in mathematical books of all nationalities.

page 316 note * On p. 366. 1. 20 (cf. pp. 206, 216), it would be better to put lower limit for minimum (which generally means an attained lower limit).