Peano Axioms (1889)
lN designates the set of natural numbers
l0 is a particular natural number in N
lS is a function S: N¨N, such that:
lFor all x ë N S(x) != 0.
lFor all x, y ë N S(x) = S(y) implies x = y.
lIf P is any predicate, such that
lP(0)
lfor all x ë N P(x) implies P(S(x))
then
for all x ë N P(x). Giuseppe
Peano, 1858-1932