# Arithmetic/Types of Numbers/Integer Number

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An integer number is any of: a positive whole number (a positive integer), a negative whole number (a negative integer), or zero.

### Positive Integer[edit | edit source]

A Positive Integer is a natural number greater than 0, i.e. a whole number. A Positive Integer can be expressed mathematically:

- I > 0 = {+1,+2,+3,+4,+5,+6,+7,+8,+9,...}

Positive numbers are often written without a + sign:

- I > 0 = {1,2,3,4,5,6,7,8,9,...}

### Negative Integer[edit | edit source]

A Negative Integer is a negative whole number. This is represented by a - sign on the left side of the value.

- I < 0 = {-1,-2,-3,-4,-5,-6,-7,-8,-9,...}

### Number Zero[edit | edit source]

The Integers include a new number, 0.

## Rules[edit | edit source]

- a + 0 = a
- a - 0 = a
- a × 0 = 0
- a / 0 is not defined.
- a + a = 2a
- a - a = 0
- a × a = a
^{2} - a / a = 1 (except for a = 0, which is not defined, see rule 4)
- a - (-a) = 2a
- a × (-a) = - a
^{2} - a / (-a) = -1 (except for a = 0, which is not defined, see rule 4)