Real numbers

Definition

Real numbers include all rational and irrational numbers, encompassing integers, fractions, and non-repeating decimals. They can be represented on a number line.

5 Must Know Facts For Your Next Test

1. Real numbers are used to measure continuous quantities.
2. The set of real numbers is denoted by the symbol $\mathbb{R}$.
3. Any real number can be positive, negative, or zero.
4. The square root of any positive real number is itself a real number.
5. Every integer is also a real number, but not every real number is an integer.

Review Questions

• Can all real numbers be plotted on a number line?
• What distinguishes rational numbers from irrational numbers within the set of real numbers?
• Is the square root of -1 considered a real number?

Related terms

Rational Numbers: Numbers that can be expressed as the quotient or fraction $a/b$ where $a$ and $b$ are integers and $b \neq 0$.

Irrational Numbers: Numbers that cannot be expressed as simple fractions; their decimal expansions are non-repeating and non-terminating.

$\mathbb{R}$ (The Set of Real Numbers): \text{The set containing all rational and irrational numbers.}