Peano's postulates

Peano's postulates

[pā′än·ōz ′päs·chə·ləts]
(mathematics)
The five axioms by which the natural numbers may be formally defined; they state that (1) there is a natural number 1; (2) every natural number n has a successor n +; (3) no natural number has 1 as its successor; (4) every set of natural numbers which contains 1 and the successor of every member of the set contains all the natural numbers; (5) if n += m +, then n = m.