Integers Definition With Easy Examples | What Are Integers

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Definition Of Integers

Integers are a set of natural numbers that include zero and negative natural numbers.
For example:…,-3,-2,-1,0, 1, 2, 3,…. We can write an integer as a product of prime numbers. Also we can find the HCF and LCM of two integers by first writing each one as a product of prime numbers.
The collection of integers is symbolized by Z, where Z stands for Zahlen, which means “to count.”

Types of Integers

After understanding the Integers definition, let’s understand different types of Integers. There are 3 types of Integers, which are explained below:

  1. Positive integers (Z+)
  2. Negative Integers (Z-)
  3. Zero Integer (0)
Positive Integers:

Any number greater than zero is referred to as a positive number, and in this context, positive integers are counting numbers or natural numbers. It is represented by the symbol ‘Z+’. Positive integers are found on the number line to the right of zero.

As an example: Z+ = { 1, 2, 3,…,∞ }

Negative Integers:

Any number less than zero is considered a negative number, and the negative of natural numbers is referred to as a negative integer. They are denoted by the letter ‘Z-‘. The negative integers are on the number line to the left of zero.

For instance – Z- = {-∞,…,-3,-2,-1}

Zero Integer

Zero (0) is neither positive nor negative. It is referred to as a neutral number for a reason: it lacks the signs ‘+’ and ‘-‘.

Important: Negative integers are also known as the additive inverses of positive integers.

Integers on a Number Line


Video Explanation of Integers

FAQ: Integers Definition

Q1. Is “0” an Integer?

Ans. No, Zero is not an Integer, it is a neutral number.

Q2. Is a decimal number, say 1.5, an Integer?

Ans. An integer, also known as a “round number” or “whole number,” is any positive or negative number that does not contain any decimal or fractional parts. For example, 3, -10, and 59 are Integers but 1.5, -46.2, 4/9, and 2/3 are not Integers.

Q3. Are Integers also Rational Numbers?

Ans. Yes, any integer can be converted cleanly into a fraction and is a rational number.

Q4. Is every Integer a Real Number?

Ans. Integers are real numbers, but not all real numbers are integers. Here are some examples of distinctions: Real numbers include integers as well as rational, irrational, whole, and natural numbers.

Q5. Are Square Roots Integers?

Ans. Integers are the square roots of perfect squares (e.g., 0, 1, 4, 9, 16). In all other cases, positive integer square roots are irrational numbers with non-repeating decimals in their decimal representations.

Like Integers definition, if you want to know about the Definition of natural numbers, then please check this article –What are Natural Numbers?

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