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} \}

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

Question	Answer
Real numbers	All the numbers that can be found on a number line, including both rational and irrational numbers.
What is the opposite of a real number?	A complex number (which includes the imaginary unit i).
How can a real number be defined in terms of parts?	A real number is any number with only a real part (no imaginary part, so no coefficient of i).
What symbol denotes the set of real numbers?	\mathbb{R}
How is the set of real numbers defined in set-builder notation?	\mathbb{R} = \{ x \mid x \in \mathbb{Q} \text{ or } x \in \mathbb{I} \}
What is the range of values contained in \mathbb{R}?	\mathbb{R} = -\infty, \ldots, +\infty
Why is i^2 an example of a real number?	It simplifies to -1, which is real.
Give three examples of real numbers.	-10, 0, 3.14
Give three non-examples of real numbers.	i (imaginary constant), 3 + 4i (complex number), -2i (pure imaginary number).