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What is an Integer - Definition, Meaning, Addition, Subtraction and Application

In mathematics, integers are numbers that can be positive, negative, or zero but are not fractions. We use these numbers in addition, subtraction, multiplication, and division, among other mathematical operations. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. The letter Z denotes integers.

The set of integers comprises zero, whole numbers, natural numbers (also known as counting numbers), and their additive inverses in terms of sets (-1,-2,-3,-4,-5,..). Real numbers are subdivided into integers.

In mathematics, we have different numbers, such as -

  • Real Numbers
  • Natural Numbers
  • Whole Numbers
  • Rational Numbers
  • Irrational numbers
  • Even & Odd Numbers, etc.

You may also want to know about roman numerals?

What are integers?

An integer is derived from the Latin word integer, which means "whole." It is a particular set of whole numbers represented by the letter Z that consists of zero, positive numbers, and negative numbers.
Integer Examples: 9, 15.
This set of numbers does not include fractions, decimals, or percentage.


The following are the rules for integers:

An integer is the sum of two positive integers.
A positive integer is equal to the sum of two negative integers.
An integer is the product of two positive numbers.
An integer is the product of two negative integers.
An integer's sum and inverse are equal to zero, while an integer's reciprocal is equal to one.
Let's look at some examples of signed integer numbers being added, subtracted, multiplied, and divided.

Signed Integer Numbers Addition

Add the absolute values to the two integers with the same sign, then write the sum with the sign supplied with the numbers.

Addition and Subtraction of Signed Integers

Change the sign of the second number being subtracted and follow the addition rules when subtracting two integers.
Division and Multiplication of Signed Integer Numbers
The rule for multiplying and dividing two integers is straightforward.
The outcome is positive if both integers have the same sign.
If the signs of the numbers disagree, the outcome is negative.


Integers are more than simply numbers on a piece of paper; they have a wide range of practical uses. In the actual world, positive and negative numbers have various effects. They're mostly used to represent two opposing circumstances.

Positive numbers are used to represent the temperature when it is above zero, and negative numbers indicate the temperature when it is below zero. They allow you to compare and measure two things, such as how large or tiny something is, or how many more or fewer items there are, and so they help to quantify things.

Players' scores in golf, football, and hockey competitions, movie or song ratings, and bank credits and debits are all examples of real-life scenarios where integers are used.


What exactly are integers?

Integers are made up of zero, natural numbers, and the additive inverse of those numbers. Except for the fractional component, it may be expressed on a number line. It is indicated by the letter Z.

What is the definition of an integer formula?

An integer is a collection of positive and negative integers, as well as zero, that has no formula.

What are some integer examples?

Integers can be 3, -5, 0, 99, -45, and so on.

Is it possible for integers to be negative?

Negative integers, such as -1,-2,-3,-4,-5, and so on, are the additive inverses of natural numbers.

What are the different kinds of integers?

There are three types of integers:
Negative integers, positive integers, and zero

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