Set of Rational Numbers

Set of Rational Numbers

The set of numbers obtained from the quotient of a and b where a and b are integers and b is not equal to 0.

Symbol

The set of rational numbers is denoted by the symbol \(\mathbb{Q}\).

  • The set of positive rational numbers : \(\mathbb{Q}\)\(_{+}\) = {x ∈ \(\mathbb{Q}\) | x ≥ 0}
  • The set of negative rational numbers : \(\mathbb{Q}\)\(_{–}\) = {x ∈ \(\mathbb{Q}\) | x ≤ 0}
  • The set of strictly positive rational numbers : \(\mathbb{Q}\)\(_{+}^{*}\) = {x ∈ \(\mathbb{Q}\) | x > 0}
  • The set of strictly negative rational numbers : \(\mathbb{Q}\)\(_{–}^{*}\) = {x ∈ \(\mathbb{Q}\) | x < 0}

All natural numbers, integers and decimals are rational numbers.

Examples

The following numbers are rational numbers :

  • \(\frac{3}{4}\)
  • –\(\frac{1}{3}\)
  • 5
  • –7

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