We think you are located in United States. Is this correct?

The real number system

Practise now to improve your marks

You can do it! Let us help you to study smarter to achieve your goals. Siyavula Practice guides you at your own pace when you do questions online.

Sign up to improve your marks

1.2 The real number system (EMA3)


We use the following definitions:

  • \(\mathbb{N}\): natural numbers are \(\left\{1; 2; 3; \ldots\right\}\)

  • \(\mathbb{N}_0\): whole numbers are \(\left\{0; 1; 2; 3; \ldots\right\}\)

  • \(\mathbb{Z}\): integers are \(\left\{\ldots; -3; -2; -1; 0; 1; 2; 3; \ldots\right\}\)

The following video shows an example of determining which of the above sets of numbers a particular number is in.

Video: 2DBH

Not all numbers are real numbers. The square root of a negative number is called a non-real or imaginary number. For example \(\sqrt{-1}\), \(\sqrt{-28}\) and \(\sqrt{-5}\) are all non-real numbers.