What does $n\gg 0$ mean in abstract algebra?

Question

I am reading this book's page 144.

While defining polynomial rings the author uses notation $n\gg 0$. I know that it means very very greater than but in this context it doesn't seem to mean that.

What does it mean in this context?

Thank you!

Answer 1

It means "for $n$ sufficiently large". For example, in this context, there exists $N>0$ so that for $n>N$, $f(n)=0$.

Answer 2

It seems to mean '' there exists $N\in\mathbb N$ such that $f(n)=0$ for $n \geq N$ ''. This is usually written '' for $n$ large enough '', I don't believe this notation is standard.