Realm of Numbers

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.