Introductory Algebra for College Students (7th Edition)

a) natural numbers: $\{ \sqrt{4} \}$ b) whole numbers: $\{ 0,\sqrt{4} \}$ c) integers: $\{ -6,0,\sqrt{4} \}$ d) rational numbers: $\{ -6,0,0.\overline{7},\sqrt{4} \}$ e) irrational numbers: $\{ -\pi,\sqrt{3} \}$ f) real numbers: $\{ -6,-\pi,0,0.\overline{7},\sqrt{3},\sqrt{4} \}$
a) Natural numbers include the numbers $\{1,2,3,4,...\}.$ Hence, from the given set, the natural number is \begin{array}{l}\require{cancel} \{ \sqrt{4} \} .\end{array} b) Whole numbers include the numbers $\{0, 1,2,3,4,...\}.$ Hence, from the given set, the whole number is \begin{array}{l}\require{cancel} \{ 0,\sqrt{4} \} .\end{array} c) Integers include the numbers $\{...,-3,-2,-1,0, 1,2,3,...\}.$ Hence, from the given set, the integers are \begin{array}{l}\require{cancel} \{ -6,0,\sqrt{4} \} .\end{array} d) Rational numbers are numbers that can be expressed as the ratio between two integers. Hence, from the given set, the rational numbers are \begin{array}{l}\require{cancel} \{ -6,0,0.\overline{7},\sqrt{4} \} .\end{array} e) Irrational numbers are numbers that CANNOT be expressed as the ratio between two integers. Hence, from the given set, the irrational numbers are \begin{array}{l}\require{cancel} \{ -\pi,\sqrt{3} \} .\end{array} f) Real numbers are all the numbers that can be represented in the real number line. Hence, from the given set, the real numbers are \begin{array}{l}\require{cancel} \{ -6,-\pi,0,0.\overline{7},\sqrt{3},\sqrt{4} \} .\end{array}