Exercise 1.9.9. Write as the ratio of two integers: −19. 8.41. Answer. Let's look at the decimal form of the numbers we know are rational. We have seen that every integer is a rational number, since a = a 1 for any integer, \ ( a\). We can also change any integer to a decimal by adding a decimal point and a zero.. Of course, if we name something the real numbers, there must be numbers that aren't real. Otherwise, they'd just be called the numbers. One such not real number, one that cannot be a length, is − 1 − 1. It is part of a collection of numbers called the complex numbers, it is denoted with the letter i i. As an extension, the square root of.

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1.1 The Real Number System

In other words, a real number is any rational or irrational number, including positive and negative whole numbers, integers, decimals, fractions, and numbers such as pi ( π) and Euler's number ( e ). In contrast, an imaginary number or complex number is not a real number. These numbers contain the number i, where i2 = -1.. of addition For any real number a, a + (− a) = 0 − a is the additive inverse of a A number and its o p p o s i t e add to zero. of multiplication For any real number a, a ≠ 0 a · 1 a = 1 1 a is the multiplicative inverse of a A number and its r e c i p r o c a l multiply to one. of addition For any real number a, a + (− a) = 0 − a is.