# Cormen Edition 3 Exercise 3.1 Question 3 (Page No. 53)

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Explain why the statement, “The running time of algorithm A is at least $O(n^2),$” is meaningless.

## Related questions

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We can extend our notation to the case of two parameters $n$ and $m$ that can go to infinity independently at different rates.For a given function $g(n,m)$, we denote by $O(g(n,m))$ the set of functions $O(g(n,m))$ $=$ {$f(n,m) :$ there exist positive constants $c,n_0,$ and ... $n \geq n_0$ or $m \geq m_0$ } Give corresponding definitions for $\Omega(g(n,m))$ and $\Theta(g(n,m))$.
Prove that $o(g(n)) \cap \omega(g(n))$ is the empty set.
Prove that the running time of an algorithm is $\Theta (g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n))$.
Is $2^{n+1} = O(2^n)$? $2^{2n} = O(2^n)$?\$