June 1, 2011 - 19:19 — Anonymous

Publisher:

Carus Publishing

Year:

2006

ISBN:

978-0-8126-2744-X and 0-8126-2744-X

Price (tentative):

USD 8.95

MSC main category:

00 General

Review:

This small booklet brings the reader to a strange place called Numberland, where all the (integer) numbers live in a big hotel. An experienced reader soon recognizes that the hotel presented here is nothing other than a version of the famous Hilbert hotel, which was constructed as a tool to illustrate the problems in connection with countability. The small size of the book, the style of writing, a (large) number of illustrations and especially the “fairy-tale-like” language all indicates that the booklet is meant for children, probably around or under ten years of age.

And at this point the reviewer was beginning to get a little unsure as to whether this rather difficult piece of mathematics should be presented and explained to children of that age. Maybe, the children should first become reliably accustomed to the notions of “more than”, “larger”, and even “finitely and infinitely many", and only after that, at a proper age, should they be faced with facts like “there are as many odd integers as there are integers” or “there are as many integer fractions as integers themselves”, which are the main “results” of the book. Also, since the concept of uncountability is not at all addressed (which is correct), the child reader can possibly be driven to the misleading realization that all infinite sets are “equally large”. So there remains a small question if the topic is suitable for children of a “fairy-tale” age. However, if the answer to this question is “yes”, then nothing can stop the reviewer from claiming that the booklet is written in a very nice way, presenting all the ideas clearly (at least for the adult reader) and in a concise yet comprehensive form.

Reviewer:

mrok