Exercise 59 Page 430

All real numbers are classified into different number sets. Within the category of real numbers, we have the following subsets of numbers. |r|l| [-0.8em] -3pt Type of& [-0.5em] Number & & Number Set -5pt [0.4em] [-0.8em] -3pt Whole& [-0.5em] Numbers & & -3pt { ,1,2, ... } -3pt [0.4em] [-0.8em] Integers & -3pt { ..., -1, ,1,2, ...} -3pt [0.4em] [-0.8em] -3pt Rational& [-0.5em] Numbers & & -3pt { ..., - 32,-1, ,1,2, ...} -3pt [0.6em] [-0.8em] -3pt Real& [-0.5em] Numbers & & -3pt { ..., - 32,-1, ,1,sqrt(2),2,π , ...} -3pt [0.6em] As we can see, the whole numbers are a part of the integers, the integers are a part of the rational numbers, and the rational numbers are a part of the real numbers. Another way to represent these sets is with a Venn diagram.

Irrational numbers are the real numbers that cannot be expressed as the ratio between two integers. A few examples are given below. - sqrt(2), π and sqrt(5) As we can see, irrational numbers can be both positive and negative. Therefore, its sometimes true that an irrational number is negative.