Linear Equations

Abstract

Since the purpose of this book is to help those students who have a weak background in mathematics to understand applications in economics and business studies, it is useful to start by reviewing some basic concepts. One fundamental idea is that of a number. The type of number that is familiar in everyday life is known as a real number. That is, it can be used to represent something ‘real’, such as 2 and 3 representing the numbers of people in two cars. In this case the numbers are positive whole numbers or positive integers, and are part of the familiar sequence 1, 2, 3, 4, … where the three dots indicate ‘and so on’. The positive integers increase without limit and are said to be unbounded. They are used in counting. If the sequence is continued in the negative direction the values are 0, −1, −2, −3, … Below we will see that the value zero is rather special in that it does not satisfy some of the standard rules of algebra, and can be interpreted as being positive or negative or neither. The numbers −1, −2, −3, … are the negative integers and while their interpretation is less obvious than for positive integers, they are familiar for measuring sub-zero temperatures and in economics they can represent debts (negative assets) or losses (negative profits).