In my class, we have defined that $$ f(x) \ll g(x) $$ on $A$ if there exist a strictly positive c such that $$ |f(x)| \le cg(x) $$ for every $x$ on $A$.
I'm a bit confused. Say that $ f(x) = x$ and $ g(x) = \frac x2 $ We could take $c = 3$, and that would mean that $x\ll\frac x2$? I'm confused, it doesn't make sense to me.