What Are Integers?
The set of all whole numbers — positive, negative, and zero. They do not include fractions or decimals.
Integers show up in real life all the time — think about temperatures below freezing, floors below ground in a building, or a bank account that goes into debt. Whenever we need to talk about amounts less than zero, we use negative numbers.
The integers can be split into three groups:
- Positive integers: 1, 2, 3, 4, 5, … (to the right of zero on the number line)
- Zero: neither positive nor negative
- Negative integers: −1, −2, −3, −4, −5, … (to the left of zero on the number line)
Positive integers are sometimes written with a + sign (e.g. +3), but usually we just write 3 and assume it is positive. Negative integers must have a − sign in front of them (e.g. −3).
Zero is special — it is the only integer that is neither positive nor negative. It sits right in the middle of the number line.
The Number Line
The number line is a straight line with zero in the centre, positive integers stretching to the right, and negative integers stretching to the left.
Two key rules about the number line:
- Moving right → numbers increase
- Moving left → numbers decrease
This means that even though −1 looks small, it is greater than −5, because −1 is further to the right.
Two integers that are the same distance from zero but on opposite sides of it. For example, 7 and −7 are opposites.
Ordering integers
Arrange these integers from smallest to largest:
Using the number line, the order from left to right (smallest to largest) is:
We use the symbols (less than) and (greater than) to compare them:
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