Is h(n) - f(n) in o(g(n)) Given f(n) in o(g(n)) and g(n) in O(H(n))?

[ammoun]

Hi

When we have f(n) \in o(g(n)) and g(n) \in O(H(n))

Can I proove that h(n)-f(n) \in o(g(n))?

Obviously I don't want you to give me the answer, but some hints and maybe which definitions of O and o I should use.

Thanks

 

[ammoun]

Ok, I believe I came up with a counter example:

If f(n)=n, g(n)=n^{2} and h(n)=n^{3}

When I looked for the limit of the difference / g(n) it cannot give 0.

Could you please confirm this result?

Thanks

 

[ramsey2879]

Hi

When we have f(n) \in o(g(n)) and g(n) \in O(H(n))

Can I proove that h(n)-f(n) \in o(g(n))?

Obviously I don't want you to give me the answer, but some hints and maybe which definitions of O and o I should use.

Thanks

What definitions are you talking about? Also how does H(n) relate to h(n). Forgive me for asking but I just don't know what you are referring to.

 

[ammoun]

What definitions are you talking about? Also how does H(n) relate to h(n). Forgive me for asking but I just don't know what you are referring to.

Thank you ramsey, it was the same function h and the definitions I'm talking about are of big O of a function and small o.

For example Big O of g(n) is the set of function f(n), f(n)≤c g(n). (not complete definition)