"If we take ε to be huge" just means "let's analyze the growth rate as ε goes to infinity". More formally, what's going on is that you have a function which is

"If we take ε to be huge" just means "let's analyze the growth rate as ε goes to infinity". More formally, what's going on is that you have a function which is polynomial in ε and which is always positive; therefore the leading coefficient must be positive, as if it were negative, the polynomial would be eventually negative. The question "what if it isn't huge" makes no sense; we can pick ε, it's not some external given. (Actually, as mentioned, we're not picking it to be one specific value but rather letting it tend to infinity, but that's another matter.)