If we order cars from a car manufacturer, we cannot order 10.56986 cars; we may order either 10 or 11 cars, but any value in between makes no sense. It should be intuitively clear what we mean by an integer number; integer numbers are used to measure variables that have a intrinsically discrete nature. A real number is a number with some, possibly infinite, decimal part. Real numbers are not that obvious to characterize formally, but intuitively a real variable is used to measure something that has an intrinsically continuous (or “fluid”) nature. In the following, we denote the set of real numbers by 
and the set of integer numbers by 
. If we are just interested in nonnegative numbers, we use notations 
and 
.
Fig. 2.4 The real line.
Real numbers can be represented on a real line, as illustrated in Fig. 2.4, ranging from −∞ (minus infinity) to +∞ (plus infinity). Given any pair of real numbers on the real line, you can always find a real number between them. For instance, given
we can actually find infinitely many real numbers between them; one example is x = 2.3982133. The set of real numbers is “dense,” whereas the set of integer numbers is not: There is no integer number between 10 and 11.
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