| 21. | A rigorous proof of these formulas and his assertion that such formulas would exist for all odd powers took until.
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| 22. | :I would suggest the experimental outcome you describe would in fact be a rigorous proof of the Riemann hypothesis.
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| 23. | In 1806 Jean-Robert Argand independently issued a pamphlet on complex numbers and provided a rigorous proof of the Bellavitis.
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| 24. | This was contrary to the idea of rigorous proof where all conditions need to be stated and nothing can be assumed.
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| 25. | I'd like to be a believer, but I also have to remain skeptical until we see rigorous proof ."
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| 26. | Here, too, rigorous proofs were first given after the development of richer mathematical tools ( in this case, topology ).
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| 27. | For decades, mathematicians generally thought that this proof was flawed and that the first rigorous proof was carried out by Oswald Veblen.
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| 28. | This can be used to give a rigorous proof of G�del's first incompleteness theorem, because no recursively enumerable set is productive.
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| 29. | Again, a rigorous proof is needed for the fact that e _ n does not admit an equivalent regular expression of lower star height.
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| 30. | Von Mangoldt provided a rigorous proof of an explicit formula for involving a sum over the non-trivial zeros of the Riemann zeta function.
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