| 1. | More disconcerting than the set's incompleteness is its presentation.
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| 2. | These developments left the incompleteness theorems in essentially their modern form.
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| 3. | Peano arithmetic is also incomplete by G�del's incompleteness theorem.
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| 4. | This is the key idea behind Godel's Incompleteness Theorem.
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| 5. | Penrose's argument stemmed from G�del's incompleteness theorems.
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| 6. | I also like G�del's incompleteness theorems for similar reasons.
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| 7. | They identified properties of positivity, degeneracy, incompleteness and idiosyncrasy.
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| 8. | Then G�del's incompleteness theorem pretty much answers the question.
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| 9. | But to some, the abiding incompleteness could seem disconcerting.
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| 10. | To prove the first incompleteness theorem, G�del represented statements by numbers.
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