Real numbers

Definition

Real numbers include all rational and irrational numbers, encompassing the entire set of numbers on the number line. They can be positive, negative, or zero.

5 Must Know Facts For Your Next Test

1. The set of real numbers includes both rational numbers (like fractions) and irrational numbers (like $\sqrt{2}$).
2. Real numbers are closed under addition, subtraction, multiplication, and division (except by zero).
3. Every real number can be represented as a point on the number line.
4. The decimal expansion of a real number is either terminating, repeating, or non-repeating and non-terminating.
5. Real numbers satisfy properties such as the commutative property of addition and multiplication.

Review Questions

• What types of numbers are included in the set of real numbers?
• Are real numbers closed under division? If not, what is the exception?
• How can every real number be visually represented?

Related terms

Rational Numbers:

Numbers that can be expressed as a fraction where both numerator and denominator are integers.

Irrational Numbers:

Numbers that cannot be expressed as a simple fraction; their decimal expansion is non-repeating and non-terminating.

Number Line:

A visual representation of real numbers where each point corresponds to a unique real number.