Overview
The natural numbers are the numbers that are used to count, {% 1,2,3,4 ... %}. Some authors will include the number {% 0 %} in the natural numbers, others will call the set of natural numbers with {% 0 %} the whole numbers.
Peano's Axioms
Peano's axioms were one of the first formalizations of a mathematical number system. The axioms are given below.
- {% 0 %} is a natural number
- If {% n %} is a natural number, then {% s(n) %} (the successor of {% n %}) is a natural number
- {% 0 %} is not the successor of any natural number