# Integer Definition

Any **number** that has **no fractional** part is called an **Integer.** It can be **positive or negative** as the **set** of Integers **involves** all numbers used in the **calculation**. Unlike other sets including **Natural Number** Set and Whole Number Set, **Integers** can involve **negative numbers **too.

**Note:**

Read about Prime and Square Numbers here.

**Table of Contents**

Keep in **mind** that an **integer** is a **complete** number instead of involving a **decimal or fractional part**. It **means** that this set involves **whole **(complete) **numbers** only like **3, 4, 5, -9, -10, -42**, etc. Because of the **involvement **of complete numbers **only**, it is given the **name** of Integers.

Actually, this **word** has been **derived** from a **Latin** word that means “**Whole**” or “**Intact**”. That is why it involves all numbers including **zero** that have no **decimal** or fractional part.

## Representation of the Integers

In **Mathematics**, we can write a set of **integers** represented by “**Z”** like other **number **sets. It involves all numbers from **negative** infinity to **positive** infinity. Here is the **set **of Integers that you can **look** at and have an **idea** about its **elements**.

Z = {……..,-3, -2, -1, 0, +1, +2, +3,……..}

Also, the **representation **of the Integers can be **done** on the **“Number Line”** which is also used to **learn** basic **Mathematical operations**.

**Note:**

You can read about **Number Line ** here.

Here is the representation of the Integers on this line.

### Mathematical Operations on Integers

On **Integers**, all basic **Mathematical operations** can be **implemented**. Here are those operations that can be **employed** on this specific **set** of numbers.

Every **operation** has some **basic rules** like where to **start**, how to **implement**, and others. You can **understand** those basic **rules** and implement them to **solve** the questions or **problems** related to Integers.

## Classification of Integers

Integers are **classified** into two major **categories** and **one** of those categories can be **subdivided **into two more categories. So, you can say that three **major types **of numbers come out from a** set** of Integers.

Here is the **pictorial** representation of the **classification** of Integers for better **understanding**.

### Fun Facts about Integers

**Sum**of**two positive**or**two negative**numbers is an**integer**.**Product**of**two negative**integers is a**positive integer**.**Sum**of an**integer**with its**inverse**form will be**zero**.**Product**of an**integer**with its**inverse**will be**1**.**Product**of an**integer**with**0**will be equal to**0**.**Addition**of an**integer**with**0**is the**number**itself- The
**additive**inverse of a**number**is the**inverse**number of the**original one**. - An
**integer**can never have a**decimal portion**. - The
**set**of integers can**involve**negative**numbers too**.

### FAQ's

**Is 0 an integer?**

Yes, 0 is the part of a set of integers.

**Is 0 a positive number or a negative number?**

0 has no significance in this regard. It is neither a positive number nor a negative number. 0 is considered a whole number only.

**Do integers involve negative numbers too?**

Yes, integers involve all the real numbers found till now. It involves the whole numbers from negative infinity to positive infinity.

**What are the types of integers?**

There are three major types of integers mentioned below.

**What is the difference between prime numbers and composite numbers?**

- Negative numbers
- Natural numbers
- Zero

**What is the opposite of integers?**

We can’t say that a set is opposite to integers. But fractions and decimal numbers are considered to be opposite for this set of numbers.