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Mathematical Analysis and Sequences 
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#1
Apr412, 02:11 AM

P: 5

1. The problem statement, all variables and given/known data
The problem is: Show that a_{n} [itex]\rightarrow[/itex] [itex]\infty[/itex] iff for all [itex]\Delta[/itex] > 0, [itex]\exists[/itex]N such that n [itex]\geq[/itex] N [itex]\Rightarrow[/itex] a_{n} [itex]\rightarrow[/itex] [itex]\infty[/itex] 2. Relevant equations Not sure if there are any 3. The attempt at a solution I can't really think of anything to do here because I have absolutely no clue what [itex]\Delta[/itex] is meant to be my only guess was the difference between the sequences a_{n} and a_{N}... and I can't conceptualize this either. EDIT: I did some google searching, and I understand what this definition means but I have no idea how to approach it. One idea I have is that it is similar to the definition of a limit I could possibly use something along the lines of a general limit proof to prove this statement. 


#2
Apr412, 06:26 AM

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P: 39,353

That really makes no sense. What does "for all [itex]\Delta> 0[/itex]" mean when there was no "[itex]\Delta[/itex]" in the statement of the limit? And what is the difference between [itex]\Delta> 0[/itex] and [itex]n> N[/itex]?



#3
Apr512, 12:48 AM

P: 5

Yeah, so I looked a lot more into it, and it turns out it's just the definition of diverging to infinity except with worser notation. This was word for word a homework probably, btw...



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