In this book, Asimov takes you through the development of numbers, from the initial set of positive integers through the transfinite alephs. The progression is logical, he first establishes the infinitude of the positive integers and then explains the reasons why negative numbers are needed. Along with the negative integers, he explains the basic rules of addition, subtraction, multiplication and division as applied to integers. Subtraction is used to justify the need for negative integers and then division to explain the need for fractions. Asimov uses the applications for commerce to describe how negative numbers and fractions came to be accepted. After fractions are covered, he then goes on to explain infinite decimals, starting with those that repeat and then to the ones that do not. Complex numbers are next, although here, he is somewhat limited in the explanation of the details in how arithmetic is done on complex numbers. Written at the level of the middle school student, Asimov is once again at his best, explaining the various categories of numbers and showing why they are needed in the modern world. This book is very suitable reading for students at that level.
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