Integers: Definition, Operations, and Worked Examples

An integer is any number from the set of negative numbers, zero, and positive numbers, with no fractional or decimal part.

Examples: -3, -2, -1, 0, 1, 2, 3, continuing endlessly in both directions. A number such as 2.5 or a half is not an integer because it has a fractional part.

Types of Integer

Zero holds a special position: it is the boundary between positive and negative, and belongs to neither.

The Number Line

The number line is the main tool for understanding integers. Zero sits in the middle, positives to the right, negatives to the left. The further right, the greater the value.

From this comes a rule that often confuses: -5 is smaller than -2, even though 5 is bigger than 2. The reason is visible immediately on the line - the position of -5 lies further left.

A way to check through real context: -5 degrees is colder than -2 degrees, and a debt of 5 million is heavier than a debt of 2 million.

Integers in Everyday Life

• Air temperature. Minus 3 degrees on a mountain top.
• Building floors. Floor -2 means two levels below ground.
• Account balance. A negative balance means debt.
• Sea depth. A depth of 40 metres is often written as -40 relative to sea level.
• Game scores. Points can fall below zero.