Integers and Natural Numbers

Numbers | A History of Numbers | Propositional Logic | Logical Completeness | The Liar's Paradox
Logical Consistency | Basic Methods of Mathematical Proof | Integers and Natural Numbers
Rational Numbers | Irrational Numbers | Imaginary Numbers | The Euler Equation

God made the integers; everything else is the work of man.
- Leopold Kroenecker

Counting is where mathematics starts. From a very young age children learn to count: one, two, three, four, five, six, seven, eight, nine, ten...

This series is the beginning of the counting numbers. You can keep counting like that forever. The counting numbers can also be called natural numbers - they're natural in the sense that they developed first.

Then there are negative numbers. If you add a negative number to its positive counterpart then you get zero - for example, -2 + 2 = 0.

The collection of all the whole numbers - the counting numbers, zero and negative numbers - are called the 'integers'. Within the set of integers you can add, subtract and multiply as much as you like and be certain of getting an integer out of the operation. You cannot, however, divide as freely. While, for example, 12 ÷ 4 = 3, if you divide 1 by 2, you get 1 ÷ 2 = 0.5, which is not an integer, it is a rational number.