# Homework Help: Mathematical Analysis and Sequences

1. Apr 4, 2012

### mercrave

1. The problem statement, all variables and given/known data

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

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 $\Delta$ 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.

Last edited: Apr 4, 2012
2. Apr 4, 2012

### 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 $n> N$?

3. Apr 5, 2012

### 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...

4. Apr 5, 2012

### micromass

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