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