Prove or disprove the following implication (Big O Notation)

Question

I couldn't prove this:

f(n) = O(g(n)) implies f(n)^k = O(g(n)^k)

where k is element of the natural, positiv numbers

I've found similar examples on the internet. But I'm not sure if it's right to implement those solutions for this example.

that's the similar example I've found http://stackoverflow.com/questions/12361448/i-need-help-proving-that-if-fn-ogn-implies-2fn-o2gn — Elfie, Apr 27 '16 at 10:33
Pleasantries will be removed. Rolling back my edits will have no effect as others will take my place. — graham.reeds, Apr 27 '16 at 10:40
@PaulHankin - k is an element of the natural, positiv numbers — Elfie, Apr 27 '16 at 11:49

score 1 · Accepted Answer · answered Apr 27 '16 at 11:15

1

Go back to the definition of big-o.

f(n) = O(g(n)) <=> \exists M \in R+,
                   \exists n_0 \in N,
                   such that:
                   \forall n > n_0
                   |f(n)| < M.|g(n)|

It is obvious that if k > 0 then |f(n)|^k < (M.|g(n)|)^k.

If k < 0, the relation is inversed.

answered Apr 27 '16 at 11:15

fjardon

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considering the big-o notation, I've found another interesting problem. http://stackoverflow.com/questions/23492509/big-o-notation-algebra/23493414#23493414 I only need to know if the prove of the second question is correct? – Elfie Apr 27 '16 at 12:02

Prove or disprove the following implication (Big O Notation)

1 Answers1