PREFACE TO THE TENTH EDITION

The changes in the present edition are as follows:

1. An index has been added. Hardy had begun a revision of an index compiled by Professor S. Mitchell; this has been completed, as far as possible on Hardy's lines, by Dr T. M. Flett.

2. The original proof of the Heine-Borel Theorem (pp. 197–199) has been replaced by two alternative proofs due to Professor A. S. Besicovitch.

3. Example 24, p. 394 has been added to.

PREFACE TO THE SEVENTH EDITION

The changes in this edition are more important than in any since the second. The book has been reset, and this has given me the opportunity of altering it freely.

I have cancelled what was Appendix II (on the ‘O, o, ~’ notation), and incorporated its contents in the appropriate places in the text. I have rewritten the parts of Chs. VI and VII which deal with the elementary properties of differential coefficients. Here I have found de la Vallée-Poussim's Cours d'analyse the best guide, and I am sure that this part of the book is much improved. These important changes have naturally involved many minor emendations.

I have inserted a large number of new examples from the papers for the Mathematical Tripos during the last twenty years, which should be useful to Cambridge students. These were collected for me by Mr E. R. Love, who has also read all the proofs and corrected many errors.