| 11. | Real numbers can be constructed as Dedekind cuts of rational numbers.
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| 12. | In general, this is an operation on fractions rather than on rational numbers.
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| 13. | The recursion can also be viewed as defining rational numbers for all integers,.
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| 14. | The rational numbers ( including 0 ) also form a group under addition.
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| 15. | Thus, when the ring R is the ring of rational numbers, one has
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| 16. | Infinite divisibility alone implies infiniteness but not uncountability, as the rational numbers exemplify.
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| 17. | The integers are a discrete ordered ring, but the rational numbers are not.
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| 18. | Energy and momentum variables are restricted to a certain set of rational numbers.
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| 19. | Therefore every positive rational number appears exactly once in this tree.
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| 20. | All rational numbers are real, but the converse is not true.
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