Mathematical Analysis and Sequences

mercrave

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.

HallsofIvy

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]?

mercrave

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...

micromass

Then your homework doesn't make much sense...