3.G rowth of Functions. 3.1 Asymptotic notation . g ( n ) is an asymptotic tight bound for f ( n ). ``=’’ abuse. The definition of required every member of be asymptotically nonnegative. Example: . In general, . asymptotic upper bound. asymptotic lower bound . Theorem 3.1.
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g(n) is an asymptotic tight bound for f(n).
For any real x
For any integer n
For any real n>=0, and
integers a, b >0
a mod n =a - a/n n.
For example, if , then