| 1. | This may require a separate transfinite induction argument to justify rigorously.
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| 2. | He called the cardinal numbers of these infinite sets transfinite cardinal numbers.
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| 3. | Then transfinite induction tells us that P is true for all ordinals.
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| 4. | Hartman, following Georg Cantor, uses reciprocals of transfinite cardinal numbers.
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| 5. | This is an example of a construction by transfinite recursion.
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| 6. | Fekete dedicated the majority of his scientific work to the transfinite diameter.
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| 7. | The constructible hierarchy, L is defined by transfinite recursion.
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| 8. | Transfinite networks extend the idea of infinite networks even further.
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| 9. | Such networks of infinite networks are called transfinite networks.
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| 10. | But there's no excuse not to be comfortable with transfinite induction!
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