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.

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.

  • Addition of Integers
  • Subtraction of Integers
  • Multiplication of Integers
  • Division of Integers

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.

Related Definitions