| 21. | Transfinite induction can be used not only to prove things, but also to define them.
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| 22. | He then proves by transfinite induction on these ordinals that no proof can conclude in a contradiction.
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| 23. | I used to fish out metal slides from Transfinite 18 : 55, 24 January 2007 ( UTC)
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| 24. | This group of definitions is dyadic fractions; a wider universe is reachable given some form of transfinite induction.
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| 25. | Zermelo proposed in 1908 the inclusion of urelements, from which he constructed a transfinite recursive hierarchy in 1930.
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| 26. | In neither of these papers did he apply his transfinite recursive method to construct the universe of all sets.
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| 27. | All primary source information ( including photos ) was just edited out of the Sweetest Day page by Transfinite.
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| 28. | The only reason I can see to prefer it is if you're not comfortable with transfinite induction.
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| 29. | Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of " infinity ".
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| 30. | The paradox of Hilbert's Grand Hotel can be understood by using Cantor's theory of transfinite numbers.
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