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Negation of limit definition 
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#1
Sep2007, 02:22 PM

P: 34

1. The problem statement, all variables and given/known data
I'm trying to show that a sequence does not have a limit, so that would mean proving the negation of the limit definition is true, right? Is this a correct negation of the definition of what it means for a sequence to have a limit? 2. Relevant equations The definition of the limit of a sequence [tex](x_n)[/tex]. The sequence [tex](x_n)[/tex] converges to [tex]L[/tex] if given [tex]\epsilon > 0[/tex], [tex]\exists K(e) \in \mathbb{N} \ni[/tex] if [tex]n > K(e)[/tex], then [tex]x_nL < \epsilon[/tex]. 3. The attempt at a solution The limit of a sequence [tex](x_n)[/tex] is not L if [tex]\exists \epsilon > 0 \ni \forall K \in \mathbb{N}[/tex], [tex]\existsn \in \mathbb{N} \ni n > K \ni x_n  L \geq \epsilon[/tex]. 


#2
Sep2007, 02:39 PM

Sci Advisor
HW Helper
P: 2,482

I think that is right, except it seems as if you have used too many N's, \in's or \ni's.



#3
Sep2007, 03:49 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363

That only has to be true for some n> Ke) 


#4
Sep2007, 08:17 PM

P: 34

Negation of limit definition
Yes, it all seems right now I guess. Thanks! and oh yeah, i guess while editting, i left in a few extra symbols...



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