2009
09.13

## Real Numbers

The numbers 1, 2, 3, … form the set of positive integers

$\left \{ 1,2,3,\ldots \right \}$

The numbers …, -3, -2, -1 form the set of negative integers

$\left \{ \ldots,-3,-2,-1 \right \}$

The set of integers consists of the set of positive integers, the set of negative integers and 0

$\left \{ \ldots,-3,-2,-1,0,1,2,3,\ldots \right \}$

The set of rational numbers consists of the numbers that can be written as a quotient of two integers $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. We cannot divide by zero. All integers are rational; 2 is because $2 = \frac{2}{1}$

Rational numbers can be represented by decimal number that terminate (e.g. $\frac{3}{4} = 0.75$), or by nonterminating repeating decimals (e.g. $\frac{2}{3} = 0.666\ldots$). Numbers that are represented by nonterminating nonrepeating decimals are called irrational numbers. An irrational numbers cannot be written as an integer divided by an integer (e.g. $\pi$, $\sqrt{2}$). Together, the rational numbers and the irrational numbers form the set of real numbers.