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The Real Number System

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1.2 The real number system (EMA3)

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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.