When you work with real numbers, you do so according to a set of rules that mathematicians often describe as properties. The properties of a number system pertain to how the numbers behave when you carry out operations using them. Figure 2.6 illustrates the basic properties of the real numbers. These properties apply to all the number systems you have dealt with so far. However, not all properties are applicable to all number systems. The next few sections review these properties in detail.