We are independent & ad-supported. We may earn a commission for purchases made through our links.
Advertiser Disclosure
Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.
How We Make Money
We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently of our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.

What are the Different Types of Integers?

Mary McMahon
Updated May 21, 2024
Our promise to you
All The Science is dedicated to creating trustworthy, high-quality content that always prioritizes transparency, integrity, and inclusivity above all else. Our ensure that our content creation and review process includes rigorous fact-checking, evidence-based, and continual updates to ensure accuracy and reliability.

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

Editorial Standards

At All The Science, we are committed to creating content that you can trust. Our editorial process is designed to ensure that every piece of content we publish is accurate, reliable, and informative.

Our team of experienced writers and editors follows a strict set of guidelines to ensure the highest quality content. We conduct thorough research, fact-check all information, and rely on credible sources to back up our claims. Our content is reviewed by subject-matter experts to ensure accuracy and clarity.

We believe in transparency and maintain editorial independence from our advertisers. Our team does not receive direct compensation from advertisers, allowing us to create unbiased content that prioritizes your interests.

There are a number of different ways to look at integers, and thus a number of different ways to classify them into types. Integers are sometimes called “whole numbers,” referencing the fact that an integer represents a number without a fraction or decimal. These numbers can be plotted on a number line, and they are not abstract, like the so-called “irrational numbers.” Three, for example, is an integer, while 5.87 is not, because it is represented with a decimal, and neither is ¾. π is an example of an irrational number.

One thing to be aware of when discussing integers is that the terminology surrounding these numbers is not standardized in the math community. People may use the same term to refer to different sets of numbers, for example. For wiseGEEK readers in a math class, it is advisable to go with the definition being used by the instructor.

One common grouping is the non-negative or positive integers, of the set {1, 2, 3...}. This set extends to infinity, for those who have some spare time and enjoy counting. Some people also include 0 in this set, although 0 is technically neither positive nor negative, for the set {0, 1, 2, 3...}. People may also use the term “natural numbers” to refer to the set of all positive numbers, with some people including the number zero in this term, while others do not.

Another type of integer is a negative integer. Negative integers are found in the set {-1, -2, -3...}. The set of negative numbers is also infinite in nature. An example of a negative integer might be a number such as -37 or -9,520.

The set of all integers, including positive numbers, negative numbers, and the number zero, may simply be known as “integers,” although this can sometimes result in confusion as some people may assume that one is referring only to the set of positive numbers. In math, the letter Z is sometimes used to symbolize the complete set of integers. Z stands for Zahren, the German word for “number,” reflecting the influence of German mathematicians on mathematics terminology. Z is an all-inclusive term which includes all numbers recognized as integers.

These numbers are the building blocks of mathematics. The set of positive integers, not including zero, has been used by humans for thousands of years. Zero is actually a relatively recent introduction to the mathematics world, and it proved to be a revolutionary one. The ability to represent zero paved the way to developing advanced mathematics such as algebra.

All The Science is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Mary McMahon
By Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a All The Science researcher and writer. Mary has a liberal arts degree from Goddard College and spends her free time reading, cooking, and exploring the great outdoors.

Discussion Comments
By ginSoul — On Jun 18, 2011

That’s a good point, but it looks really confusing when you type it out like that. When I was a kid, just reading about numbers didn’t help me learn math. Luckily, integer games came to my rescue. We had a computer lab and if it wasn’t for those games, I probably still wouldn’t know how to subtract correctly.

By Vegemite — On Jun 16, 2011

@ qwertyq – Good explanation. Negative integers do some strange things. An important difference between positive and negative integers is the fact that a big positive number represents a bigger amount, while a big negative number represents a smaller amount. To make it easier to understand, I’ll line some integers up in their natural order:


As you can see, when the negative numbers move to the left, they get larger, but each negative integer has a value that is less than zero. So, -3 equals three less than zero, but -1 only equals one less than zero, and therefore -1 is bigger than -3.

On the positive integer side, however, the numbers (and amounts they represent) get bigger as you go to the right. So 1 is smaller than 3.

By qwertyq — On Jun 15, 2011

I’ll add to this great article by explaining integer rules. When performing math functions, the outcome will be different depending on the mixture of integer types involved. For the sake of time, I’ll only explain Multiplication rules here.

If you multiply two or more positive integers, you get a positive product. Multiplying a positive with a negative will yield a negative, but two negatives yield a positive. And as always, any integer multiplied by zero will equal zero.

Mary McMahon
Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a...

Learn more
All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.

All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.