## Is there a limit of cos (n!)?

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Hi, I encountered a problem today to prove that cos (n!) does not have a limit. I have no idea how to do it formally. Could someone help? The simpler the proof (by that i mean less complex theorems are used) the better. Thanks

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It has a limit if the argument of the function is expressed in degrees. – Justin Melvin Nov 2 2010 at 21:01

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The question is now here: math.stackexchange.com/questions/8690/… – Douglas S. Stones Nov 2 2010 at 21:50

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The question boils down to whether the sequence $cn!$ tends to a limit mod 1, where $c=1/(2\pi)$. There are transcendental numbers $c$ for which the sequence DOES tend to a limit mod 1, so we have to use something about $\pi$. I'm sorry to see the question closed – SJR Nov 2 2010 at 22:26

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I've started a meta conversation over at meta.mathoverflow.net/discussion/741/… – David Speyer Nov 3 2010 at 1:08

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IMO it would have made sense for people to participate in the meta thread rather than to have an close/open tug-of-war with no discussion. Oh well. – Ryan Budney Nov 3 2010 at 5:31
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