My Math Forum big-O subset relationships

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 June 24th, 2011, 12:25 AM #1 Member   Joined: May 2011 Posts: 38 Thanks: 0 big-O subset relationships kinda confused with these questions, we're suppose to prove the subset relationships O(1) ? O(log2n) O(log2n) ? O(n) n log n ? O(n^m), m>1 O(c^n), c>1 ? O(n!)
 June 24th, 2011, 07:10 AM #2 Senior Member   Joined: Jun 2011 Posts: 298 Thanks: 0 Re: big-O subset relationships Show $O(1)\subseteq O(\text{log}_2n)$. If $O(1)=\emptyset$, then it's a subset of every set. If $O(1)\neq \emptyset$, then $\exists n\in \mathbb{N}(O(\log_2n))$. In particular, $n=2$, so that $O(\log_2n)=O(1)$ The last three parts follow the same concept. Get a pencil and paper, draw graphs, and make tables, then you will be able to do the rest.

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