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Set of Natural Numbers

Definition: N, the set of natural numbers

(omitted)

Proposition: N is the smallest set that satisfies the properties:

0 in N;

forall x in N: x' in N;

forall F:

(F(0) /\  forall x in N: F(x) => F(x+1)) => forall x in N: F(x).

Third Peano law is a consequence of this proposition.