Real numbers

The number system is made up of real numbers and imaginary numbers. Real numbers $\mathbb R$ are all the numbers on a number line. The real number line is infinite, which means it continues forever in both directions. Real numbers are infinite.

Real numbers are made up of all rational $\mathbb Q$ and all irrational $\mathbb {Q}^|$ numbers. 

Beginning with the natural numbers, we expand each set to form a larger set of numbers.

We use the following definitions.

The set of natural numbers $\mathbb N$ includes the numbers used for counting: {${1, 2, 3, ...}$} .

The set of whole numbers $\mathbb N_o$ is the set of natural numbers plus zero: {${0, 1, 2, 3, ...}$} .

The set of integers  $\mathbb Z$ adds the negative of the natural numbers to the set of whole numbers 
{${..., -3, -2, -1 ,0, 1, 2, 3, ...}$}. It is important to remember that integral values are not fractions.

The set of rational numbers $\mathbb Q$ includes fractions that can be written as $\frac{a}{b}$ where $a, b \in \mathbb{Z}, b \neq0$.

The set of irrational numbers $\mathbb {Q}^|$ are numbers that cannot be written as a fraction with the numerator and denominator as integers. These fractions give us non-repeating and non-terminating (they do not end) decimals.

Test your understanding of real numbers by trying the next activity.