# Proving Big Omega of a polynomial without limits

Here is the definition of $$\Omega$$:

$$f(n) = Ω(g(n))$$ iff there exist positive constants $$c$$ and $$n_0$$ such that $$f(n) \ge cg(n)$$ for all $$n\ge n_0$$.

Here is one theorem:

If $$f(n) = a_m n^m + \cdots + a_1 n + a_0$$ and $$a_m > 0$$, then $$f(n) = \Omega(n^m)$$.

I want to prove this, without using limits. Despite many hours of searching across the internet, all I could find is proofs using limits. Is there any other way?