Volume B Number Systems
In this volume the familiar system of natural numbers is introduced and discussed in Chapter 1. These numbers are used for counting discrete objects. The basic operations of addition and multiplication are also discussed. It is deficient because there is no number indicating no objects to be counted (Roman numerals had this deficiency). Moreover, the equation 5 + x = 5 cannot besolved usisng this system. In chapter 2 the system of non-negative integers is discussed. It contains zero (0). But in this system the equation 5 + x = 3 cannot be solved. Chapter 3 contains the discussion of the integers. But this system cannot provide the solution to 5x = 3. The system of rational numbers, which has the operation of division, is discussed in chapter 4. The solution to x2 = 2 requires a larger system and the system of real numbers is discussed later in chapter 4. Among the real numbers there is no solution to x2 = --1. In chapter 5 the system of complex numbers is discussed.
sqrt(2) = square root of 2 is not in that system. Finally in chapter is an optional discussion of a large numerical system called quaternions.
Click on one of the following chapters in this volume:
Chapter 1 Natural Numbers
Chapter 2 Non-negative Integers
Chapter 3 Integers
Chapter 4 Rational and Real Numbers
Chapter 5 Complex Numbers and Quaternions
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