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Asymptotic Notation in Equations

Example: 2$n^2$ + 3n + 1 = 2$n^2$ + $\Theta(n)$



In other words, there is some function f(n) element of $\Theta(n)$ that makes the equation true; namely, 3n + 1.



2$n^2$ + 3n + 1 = 2$n^2$ + $\Theta(n)$ = $\Theta(n^2)$.



In other words, for any function f(n) element of $\Theta(n)$, there is some function h(n) element of $\Theta(n^2)$; namely, 2$n^2$ + f(n).


next up previous
Next: Summary Up: l1 Previous: Theorem 2.1