| 11. | Church numerals are the representations of natural numbers under Church encoding.
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| 12. | I don't understand where boundaries for arithmetic of natural numbers lay.
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| 13. | But this is impossible, since natural numbers cannot be shrunk indefinitely.
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| 14. | Second-order arithmetic directly formalizes natural numbers and sets of natural numbers.
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| 15. | However, it also blocks one standard definition of the natural numbers.
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| 16. | Note that the natural numbers are isomorphic to lists of units.
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| 17. | Thus Dedekind infinite sets contain subsets that correspond bijectively with the natural numbers.
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| 18. | These registers hold only natural numbers ( zero and the positive integers ).
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| 19. | The second part of the program nondeterministically chooses a natural number on request.
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| 20. | Formally, a decision problem is a subset of the natural numbers.
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