Peano postulates

[Giuseppe Peano]? proposed 5 axioms that have come to be known as Peano postulates.

There is a set N known as Natural numbers, which for the following five statements are true:

• 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 different, starting at 1 instead of 0.