What is the significance of Epsilon here? Elementary analysis

  • Thread starter retspool
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  • #1
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So i am almost 3/4 through elementary analysis but i seem to be unable to comprehend the basic definition of convergence of series

this is how the defn goes.

A sequence (sn) is said to converge to a real number s provided that

for each ε > 0 there exists a number N such that n>N implies |sn - s| < ε

where lim Sn = s where Sn approaches infinity



I am able to use this definition in the homeworks and problems, but i don't know what it means.

-retspooL
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi retspool! welcome to pf! :smile:

(have an infinity: ∞ and try using the X2 icon just above the Reply box :wink:)

i assume you're happy with the epsilon-delta method for a function f(x) as x –> a where a is finite?

this is the same, except that instead of x -> a we have x -> ∞, and instead of "nested" neighbourhoods of a getting arbitrarily close to a, we have "nested" neighbourhoods of ∞ getting arbitrarily close to ∞, ie neighbourhoods of the form (N,∞) …

for any ε, we can find an interval (N,∞) in which |f(x) - s| < ε :smile:
 
  • #3
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Gotcha,

Thanks
 

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