[Giuseppe Peano]? proposed the following 5 axioms for the natural numbers; they have come to be known as the **Peano postulates**.

/Talk

- There is a natural number 0.
- Every natural number
*a*has a successor, denoted by*a*+ 1. - There is no natural number whose successor is 0.
- Distinct natural numbers have distinct successors: if
*a*<>*b*, then*a*+ 1 <>*b*+ 1. - If a property is possessed by 0 and and also by the successor of every natural number it is possessed by, then it is possessed by all natural numbers.

These axioms are sometimes paraphrased differently, starting at 1 instead of 0.

/Talk