# Mathematical Analysis and Sequences

by mercrave
Tags: analysis, mathematical, sequences
 P: 5 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.
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,497 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 $n> N$?