162 BOOK REVIEWS upper limit of a sequence {A n } is defined effectively as lim / sup A m \, but in fact the set n-co \m 5 n J stf p = {x | there exists n such that p l£ neP and x = A n } is introduced. Chapter 6, on definition by induction, will appeal to those who feel uncomfortable about this method of definition, but I feel that Chapter 7, on functions of a continuous real variable, including uniform continuity and uniform convergence, could be improved by suppression of some repetitive

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... ils in its first half. Also, an interval is defined in set notation, of course, and a lemma is given to prove its endpoints unique; it seems to me that this kind of thing raises more doubts in the mind of the average student than it resolves. This, then, is rather an unconventional book. It gives a treatment of analysis, stopping short of infinite series and differentiation, which is rigidly tied to set theory. It will appeal to some and rouse antagonism in others; that there are valuable things in Chapters 1, 2, 3 and 6, everyone will admit. The text seems to be virtually free from errors and misprints, and the layout and printing are very good.