Real numbers

Real numbers are all the numbers that can be found on a number line. This includes both rational numbers and irrational numbers.

The opposite of a real number are complex number (which include the imaginary unit i).

More simply, a real number is any number with only a real part (no imaginary part, so no coefficient of i).

Notation

The set of real numbers is usually denoted by the symbol \mathbb{R}:

\mathbb{R} = \{ x \mid x \in \mathbb{Q} \text{ or } x \in \mathbb{I} \}

Contained values

\mathbb{R} = -\infty, \ldots, +\infty

Examples of real numbers

• -10
• 0
• 3.14
• \frac{1}{2}
• \sqrt{2}
• \pi
• i^2 (simplifies to -1, which is real)

Non-examples of real numbers

• i (imaginary constant)
• 3 + 4i (complex number with real and imaginary parts)
• -2i (pure imaginary number)
• 5 - i (complex number with real and imaginary parts)