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.

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