1.1: Background regarding numbers

The natural numbers (denoted by \(\mathbb{N}\) are the numbers

\[1,2,3,4,5, \dots \nonumber \]

The integers (denoted by \(\mathbb{Z}\) are the numbers

\[\dots,-4,-3,-2,-1,0,1,2,3,4,5, \dots \nonumber \]

The rational numbers (denoted by \(\mathbb{Q}\) are the fractions \(\frac{a}{b}\) of integers \(a\) and \(b\) with \(b\neq 0\). Here are some examples of rational numbers:

\[\frac{3}{5}, -\frac{2}{6}, 17, 0, \frac{3}{-8} \nonumber \]

The real numbers (denoted by \(\mathbb{R}\) are the numbers on the real number line

Here are some examples of real numbers:

\[\sqrt{3}, \pi, -\frac{2}{5}, 18, 0, 6.789 \nonumber \]

A real number that is not a rational number is called an irrational number. Here are some examples of irrational numbers:

\[\pi, \sqrt{2}, 5^{\frac{2}{3}}, e \nonumber \]

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