Real numbers

Definition

Real numbers include all the numbers that can be found on the number line. They consist of both rational and irrational numbers.

5 Must Know Facts For Your Next Test

1. Real numbers encompass both rational and irrational numbers.
2. Rational numbers are those that can be expressed as a fraction, whereas irrational numbers cannot.
3. The set of real numbers is denoted by the symbol ℝ.
4. Real numbers can be positive, negative, or zero.
5. Every integer is a real number, but not every real number is an integer.

Review Questions

• What types of numbers are included in the set of real numbers?
• How do rational and irrational numbers differ within the set of real numbers?
• Is zero considered a real number?

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 fractions; their decimal expansions are non-repeating and non-terminating.

Integers: Whole numbers and their opposites, including zero (e.g., -2, -1, 0, 1, 2).