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Toronto Math Forum
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MAT334--2020F
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MAT334--Lectures & Home Assignments
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Chapter 1
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Definition for limit is infinity?
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Topic: Definition for limit is infinity? (Read 71 times)
Jessica Long
Jr. Member
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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.
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Victor Ivrii
Administrator
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Posts: 2553
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Re: Definition for limit is infinity?
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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
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Toronto Math Forum
»
MAT334--2020F
»
MAT334--Lectures & Home Assignments
»
Chapter 1
»
Definition for limit is infinity?