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

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

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

The set of **rational numbers** consists of the numbers that can be written as a quotient of two integers where and are integers and . **We cannot divide by zero**. All integers are rational; 2 is because

Rational numbers can be represented by decimal number that *terminate* (e.g. ), or by *nonterminating repeating decimals* (e.g. ). 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. , ). Together, the rational numbers and the irrational numbers form the set of **real numbers**.

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