Real Number

Abstract

---

• Contains both Rational Numbers (有理数) and not rational numbers
• Represented with the symbol $\mathbb{R}$ (-1, pi, 4.5)

Rational Numbers (有理数)

---

• r is rational $\leftrightarrow$ there are integers a and b such that r=a/b and b!=0
• Represented with the symbol $\mathbb{Q}$ (0.5, -23, 8.5)

Theorem 4.2.1

• Every integer is a rational number

Theorem 4.3.2

• The sum of any two rational numbers is rational

Corollary 4.2.3

• The double of a rational number is rational
• Derived from Theorem 4.3.2

Complex Number

---

• Extended form Real Number
• Represented with the symbol $\mathbb{C}$ (9.1i)