Set theory: the third millennium edition , by Thomas Jech. Pp. 769. £77. 2003. ISBN 3 540 44085 2 (Springer).

You are then told of a rule that if a card has a vowel on one side, it has an even number on the other. Which cards do you need to turn over to make sure they all satisfy this rule? The blurb speaks of 'thorough revisions that improve accessibility'; that accessibility has been improved cannot be disputed, but the thoroughness can. For example, reference is made incorrectly to a theorem 4.1; an exercise requires an understanding of idempotence although the concept is not discussed in the text; and most curiously, a section on how to solve algebraic inequalities is sandwiched in the chapter on set theory, between a description of the notation for real intervals and an explanation of indexed sets. Again, when so much has been done to improve accessibility in other sections, it is disappointing to note that the description of injections and surjections is inferior to that in many other texts; some schematic diagrams would have helped enormously.