Asymptotic Bounds

• Let f(x) and g(x) be mathematical functions.

• Definition. Function f is asymptotically bounded by g if, for some N ³ 0 and k ³ 0, the inequality

  
  
  k * | g(x) | ³ | f(x) |
  

holds for all x ³ N.

• If f is asymptotically bounded by g, we write:

  
  

f = O(g)

read "f is big Oh of g".

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