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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
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Re: O(sin n), ?(sin n), ?(sin n) complexity

Quote:
 Originally Posted by ulita Hello , Do you know examples of functions belonging crowds O(sin (n)), ? (sin (n)), ? (sin (n)) ?
I suppose it depends on the exact definitions you use. I think of O(g(n)) as the set of functions f(n) such that there exists C with
$|f(n)|\le C\cdot g(n)$
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
$|f(n)|\ge C\cdot g(n)$
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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