The natural numbers are 1, 2, 3, ...
The whole numbers are 0, 1, 2, 3, ...
The integers are the natural numbers, 0 and the additive inverses of the natural numbers: ..., −3, −2, −1, 0, 1, 2, 3, ...
The natural and whole numbers are closed under addition (the sum of any two natural numbers is a natural number) and multiplication.
The integers are closed under addition, subtraction and multiplication, but not division.