|Apr4-12, 02:11 AM||#1|
Mathematical Analysis and Sequences
1. The problem statement, all variables and given/known data
The problem is:
Show that an [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] an [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 an and aN... 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.
|Apr4-12, 06:26 AM||#2|
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]?
|Apr5-12, 12:48 AM||#3|
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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