Author Topic: Definition for limit is infinity?  (Read 71 times)

Jessica Long

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 0
    • View Profile
Definition for limit is infinity?
« 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.

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2553
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: Definition for limit is infinity?
« Reply #1 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