Natural Numbers and Integers
Natural numbers count things; integers add zero and the negatives.
About this topic
Natural numbers are the counting numbers we learn first: 1, 2, 3 and onward. They answer the question "how many?" and are the foundation for all later number systems. Adding zero and the negative whole numbers gives the integers, which let us describe temperatures below freezing, bank debts, floors below ground level and changes that go in either direction.
On a number line, integers are evenly spaced marks with zero in the middle, negatives to the left and positives to the right. Moving right means getting larger, and moving left means getting smaller. Fractions and decimals fall between these marks, which is why they are not integers. The integers are closed under addition, subtraction and multiplication, meaning that doing any of these to two integers always gives another integer, but division can escape the set: 3 ÷ 2 is not an integer.
Imagine a lift in a building with three basement levels. Starting at floor 2 and going down 5 floors lands you at floor −3, because 2 − 5 = −3. Without integers, that simple question would have no answer. Integers also appear in sports scores, golf relative to par, elevation above or below sea level and account balances.
A common misconception is that zero is a natural number in every textbook. Conventions differ, and some authors include 0 while others start at 1, so check which one your course uses. Another tip is to remember that a negative sign describes direction or opposite, not "smaller digits": −100 is far less than −1.
Key ideas
- Natural numbers are 1, 2, 3 and so on
- Integers include negatives, zero and positives
- Every integer sits at a point on the number line
Quick check
Use cases: where Natural Numbers and Integers helps
- Homework: review the key idea behind Natural Numbers and Integers before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Natural Numbers and Integers without notes.
- Visual learning: play with the interactive lab to see how Natural Numbers and Integers changes when you adjust its inputs.
- Teaching a friend: explain Natural Numbers and Integers in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Natural Numbers and Integers?
Natural numbers count things; integers add zero and the negatives.
What will I learn in Natural Numbers and Integers?
Natural numbers are 1, 2, 3 and so on. Integers include negatives, zero and positives. Every integer sits at a point on the number line.
Is Natural Numbers and Integers part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Natural Numbers and Integers lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Natural Numbers and Integers?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.