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Conjectures |
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The ratio of a concave down function and a concave up function is concave down. Counter example found by C.S., October 7th. |
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Conjecture One is true outside an interval around 0. That is, the ratio of a concave down function and a concave up function is concave down outside some interval [-a,a].
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The Bookkeeper's suggestion during Ion the Quiet's stay at the Hotel cosmos results in people bunking together. The conjecture is that there are infinitely many people in at least one of the rooms. If you disprove this conjecture, you should also find the maximum number of people in a given room. |