Landau Notation: Writing Functions in Terms of Other Functions

[flouran]

I have a rather simple question which requires a direct answer:

We have two functions, f(x) and g(x).

I know that f(x) << g(x) is the same as f(x) = O(g(x)).
But if f(x) >> g(x), how can I write f(x) in terms of g(x) using the one of the four Landau symbols ($$\Omega$$, $$\omega$$, o, or O)?

I suspect that f(x) >> g(x) means the same as f(x) = o(g(x)), but I am not sure.

 

[flouran]

f(x) >> g(x) translates as:
$$f(x) = \Omega(g(x))$$.
Although according to Knuth, using an equality in front of a Landau symbol is supposedly abuse of notation (apparently $$\in$$ is preferred).

 

[g_edgar]

I have a rather simple question which requires a direct answer:

We have two functions, f(x) and g(x).

I know that f(x) << g(x) is the same as f(x) = O(g(x)).

Actually, I would say o not O for this.

log n << n means log n is MUCH SMALLER than n, not allowed to be comparable to n.

 

[flouran]

Actually, I would say o not O for this.

log n << n means log n is MUCH SMALLER than n, not allowed to be comparable to n.

No, it's O. Look up "Vinogradov symbol" and you'll see that I am right.