Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT334--2020F
»
MAT334--Lectures & Home Assignments
»
Chapter 1
»
Definition for limit is infinity?
« previous
next »
Print
Pages: [
1
]
Author
Topic: Definition for limit is infinity? (Read 103 times)
Jessica Long
Jr. Member
Posts: 6
Karma: 0
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 − z
_{0}
| < 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.
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2555
Karma: 0
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
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT334--2020F
»
MAT334--Lectures & Home Assignments
»
Chapter 1
»
Definition for limit is infinity?