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#### find_the_fun

##### Active member

- Feb 1, 2012

- 166

- Thread starter find_the_fun
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- Feb 1, 2012

- 166

- Jan 26, 2012

- 890

To say that \(f(n,k)\in O(n+k)\) means that there exists a \(C>0\) such that for \(n+k\) large enough:

\[|f(n,k)| < C |n+k|\]

That is they jointly define the bound on the growth of \(|f(x,k)|\)

CB

- Feb 13, 2012

- 1,704

One of the basic property of the 'big-O notation' is that, if f and g are positive functions, then ...

$\displaystyle f_{1} \in \mathcal{O} (g_{1})\ \text{&}\ f_{2} \in \mathcal{O} (g_{2}) \implies f_{1}+f_{2} \in \mathcal{O} (g_{1}+g_{2}) $

Kind regards

$\chi$ $\sigma$