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## 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.