# Toronto Math Forum

## MAT334--2020F => MAT334--Lectures & Home Assignments => Chapter 1 => Topic started by: Jessica Long on September 28, 2020, 07:39:28 PM

Title: Definition for limit is infinity?
Post by: Jessica Long on September 28, 2020, 07:39:28 PM
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.
Title: Re: Definition for limit is infinity?
Post by: Victor Ivrii on September 29, 2020, 04:35:15 AM
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