What Is an Integer?
An integer is any whole number — positive, negative, or zero.
Integers: ...−3, −2, −1, 0, 1, 2, 3...
Not integers: 1/2, 0.75, 3.14, √2 (these have fractional or decimal parts)
How integers relate to other number types
Number types form a hierarchy:
- Natural numbers (counting numbers): 1, 2, 3, 4... (no zero, no negatives)
- Whole numbers: 0, 1, 2, 3, 4... (includes zero, no negatives)
- Integers: ...−3, −2, −1, 0, 1, 2, 3... (includes negatives)
- Rational numbers: any number that can be written as a fraction (includes integers, since 3 = 3/1)
Each type includes all the types above it. Every natural number is a whole number, every whole number is an integer, and every integer is a rational number.
Why integers matter
Integers appear when your child encounters:
- Negative numbers: temperature below zero, debt, below sea level
- The coordinate plane: negative x and y coordinates
- Subtraction results that go below zero: 3 − 7 = −4
- Algebra: solutions to equations like x + 5 = 2
Common confusion
"Is −3 a whole number?" No — whole numbers start at 0 and go up. −3 is an integer but not a whole number.
"Is 5.0 an integer?" Yes — 5.0 = 5, which is a whole number and therefore an integer. The decimal does not change its value.
"Is 0 positive or negative?" Neither. Zero is the boundary between positive and negative integers.
Related concepts
- Negative numbers: full teaching guide
- Number sense: understanding number relationships
- The coordinate plane: integers as coordinates