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August 17th, 2010, 12:26 AM  #1 
Newbie Joined: Aug 2010 Posts: 2 Thanks: 0  O(sin n), ?(sin n), ?(sin n) complexity
Hello , Do you know examples of functions belonging crowds O(sin (n)), ? (sin (n)), ? (sin (n)) ? 
August 17th, 2010, 06:14 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: O(sin n), ?(sin n), ?(sin n) complexity Quote:
or maybe the same but only for large enough N. So with either of those definitions, there are no functions in O(sin n), since sin n < 0 for arbitrarily large n. Using the equivalent definition for ? with it's easy to see that (among others) all functions bounded below by a positive constant are in ?(sin n). The usual definition of ?(g(n)) is usually just the intersection of ?(g(n)) and O(g(n)), right? So in that case there would be no functions in ?(g(n)). For weird cases like this, though, it's going to come down to the definitions. There are lots of definitions that are all the same for the usual functions, but differ on pathological examples.  
August 18th, 2010, 07:56 AM  #3 
Newbie Joined: Aug 2010 Posts: 2 Thanks: 0  Re: O(sin n), ?(sin n), ?(sin n) complexity
Thanks a lot. 

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