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*Definition:* **N**, the set of *natural numbers*

(omitted)

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

0 in N;forallxinN:x' inN;forallF:( F(0) /\forallxinN:F(x) =>F(x+1)) =>forallxinN:F(x).

*Third Peano law is a consequence of this proposition.*

Author: Wolfgang Schreiner

Last Modification: November 16, 1999