| 41. | Lower bounds may be derived with statistical mechanics arguments.
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| 42. | This hypothesis is used to show very many lower bounds on algorithms in computer science.
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| 43. | Of course, people lie about adultery, so those figures should be taken as lower bounds.
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| 44. | Since probabilities are non-negative this gives a lower bound.
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| 45. | Bolzano was the first to recognize the greatest lower bound property of the real numbers.
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| 46. | Adding back the lower bound gives us our ranges:
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| 47. | Lower bounds again are defined by inverting the order.
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| 48. | Again, no tight lower bound has been proven.
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| 49. | Only upper and lower bounds have been invented.
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| 50. | Radar observations place a lower bound of about.
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