Definition for limit is infinity?

[Jessica Long]

I know we defined a limit at infinity, but what about when a limit at a point is infinity?
Would this definition work: For any 𝜀 > 0 there exists 𝛿 > 0 such that |z − z₀| < 𝛿 ⇒ |f(z)| > 𝜀.
Or for limit at infinity is infinity: For any 𝜀 > 0 there exists 𝛿 > 0 such that |z| > 𝛿 ⇒ |f(z)| > 𝜀.

[Victor Ivrii]

That's right but it is a custom to denote by $\varepsilon,\delta$ something small. In this case capital letters, say $R,M$ would be better, for arbitrarily large