Exercise 53 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 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) These are all numbers that are contained within the largest area only. Therefore, the statement that an integer is an irrational number is never true.