11. In 1883, Cantor extended the natural numbers with his infinite ordinals. 12. And I would like to have categorical definition of natural numbers . 13. Throughout this article the word " number " refers to a natural number . 14. The set of computable numbers has the same cardinality as the natural numbers . 15. Other independence results concern Peano arithmetic and other formalizations of the natural numbers . 16. The set of finite lists of natural numbers is the initial such algebra. 17. These three properties were originally included among the Peano axioms for natural numbers . 18. In this sense, prime numbers occur more often than squares of natural numbers . 19. As each natural number has a unique multiplicative decomposition into powers of primes. 20. Second-order arithmetic directly formalizes natural numbers and sets of natural numbers .
