Preliminaries
All of the mathematics in this book is based on real numbers. Historically, mathematics began with the set of natural numbers (or positive integers) on which we have the operations of addition and multiplication. Much later, this set was extended by adding zero and the negative integers, thus giving the set of integers. In this set, subtraction is always possible, but division is only possible in certain cases. For example, we can divide 20 by 5, but not by 6. Mathematicians were thus led to introduce the rational numbers (or fractions), so division was always possible (except by zero). Eventually it was realised that yet more ‘numbers’ were needed to do even quite simple calculations. For example, the diagonal of a unit ...
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