Mathematical Analysis and Sequences

[mercrave]

Homework Statement

The problem is:
Show that a_n \rightarrow \infty iff for all \Delta > 0, \existsN such that n \geq N \Rightarrow a_n \rightarrow \infty

Homework Equations

Not sure if there are any

The Attempt at a Solution

I can't really think of anything to do here because I have absolutely no clue what \Delta 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 \Delta> 0" mean when there was no "\Delta" in the statement of the limit? And what is the difference between \Delta> 0 and n> N?

 

[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...