# Integers

With natural numbers,** it is not** possible to operate ** when the minuend is smaller than the subtrahend**, but in life there are such operations.

For example, the need to represent** owed money , temperature below zero and depths with respect to sea level**.

The previous examples require us to expand the concept of natural numbers and introduce a new numerical set called** integers**.

A set of integers is formed by:

** = {...−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5 ...}**

That is, the natural numbers, their opposites (negative) and the zero. They are divided into three parts: **positive integers** or natural numbers, **negative integers** and **zero**.

Since the integers contain the positive integers, the natural numbers are a subset of integers.

## Absolute Value of an Integer

The absolute value of an integer is a natural number that is obtained after the sign is removed from the integer.

The absolute values are written between vertical bars.

**|−5| = 5 **

**|5| = 5 **

## Representation of Integers

1. In a horizontal line, take any point that is designated as **zero**.

2. In equal distances to the right of zero are the positive numbers:** 1, 2, 3,... **

3. In equivalent distances to the left of zero are the negative numbers**: −1, −2, −3, ... **