Mathematical Analysis and Sequences

[mercrave]

Homework Statement

The problem is:
Show that a_n $\rightarrow$ $\infty$ iff for all $\Delta$ > 0, $\exists$N 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...