This picture book uses the idea of a hotel with infintely many rooms for introducing some advanced concepts about numbers and infinity to children. The hotel, run in the book by "Mr. and Mrs. Hilbert", was actually a metaphor attributed to the mathematician David Hilbert and has already appeared in other works of mathematical fiction for adults (see The Extraordinary Hotel... and Hilbert's Hotel). Here, in addition to the usual surprises about infinite sets, the young reader can be introduced to odd vs. even numbers, fractions, and the basic algebraic operations. Like the unrelated book Numberland by George Weinberg, most of the characters in the book are the positive integers themselves. The climax, which is well presented, is the onetoone pairing of the set of fractions with the positive integers (which in the language of Georg Cantor proves that the rational numbers are a countable set).
Thanks to Paula Morrow for bringing this unusual children's book to my attention.
A review of this book was published in AMS Notices, Jan 2009.
Contributed by
Amy Bassan
My elementary students love this book. The pictures and stories are a creative rendition of a very difficult mathematical concept. I reccomend it highly.

