Can anyone explain to me how f(n)=n^(0.999999) log n=O(n^(0.999999) n^(0.000001))?



Answered question


Can anyone explain to me how
f ( n ) = n 0.999999 log n = O ( n 0.999999 n 0.000001 )?

Answer & Explanation

Alanna Downs

Alanna Downs

Beginner2022-07-17Added 11 answers

It's because log n = O ( n α ) as n for any fixed α > 0. They chose α = 0.000001
To see this, first show that
lim n log n n α = 0
by using L'Hopital's rule. This implies
log n n α = O ( 1 ) ,
and multiplying both sides of this by n α yields log n = O ( n α )

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