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Set Theory
  1. The set of numbers \(\{1,2,3,\dots\}\) is called the set of natural numbers. It is denoted \(\mathbb{N}.\)
  2. The set of numbers \(\{0,1,-1,2,-2,\dots\}\) which contains \(0\) and all positive and negative natural numbers is called the integers. It is denoted \(\mathbb{Z}.\)
  3. The set of numbers \(\{\frac{a}{b} : a,b \in \mathbb{Z}, b \neq 0\}\) is called the rational numbers. It is denoted \(\mathbb{Q}.\)
  4. The set of all decimal expansions is called the real numbers. It includes numbers such as \(\pi\) and \(e\) which cannot be represented as fractions of integers. The real numbers are denoted \(\mathbb{R}.\) This set is more rigorously defined in real analysis.
  5. The set of numbers \(\{a + ib: a,b \in \mathbb{R}, i^2 = -1\}\) is the set of complex numbers. It is denoted \(\mathbb{C}.\)