Question

f>g means that f>=g (f dominates g) and g does not dominate f.

f>>g means that cf>g (eventually) for any c>0

What’s the difference?

Answer 1

An example:

f = 2n
g = n

You can see that f > g but f not >> g because you can choose c == 0.1 and then cf will never be > g.

However:

f = n^2
g = 2n

You can see that at first g>f but eventually f>g for large enough n and no matter how small you make c, eventually cf will become larger than g. Therefore f>>g.