If there are 2 functions say f(x) and g(x) then is it possible that both conditions:
1) f = o(g) ............small-oh
2) f = $\omega$(g) ......little omega
are satisfied at the same time?
The example which I thought of is let f(x)=x and g(x)=x+1
Now, for x>=2 or x>1
I can have:
1) f(x) > $\frac{1}{2}$g(x)
2) f(x) < 2.g(x)
This means I can have c1.g < f < c2.g for which we have no asymptotic notation.
Please help if I am going wrong somewhere.