1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical Analysis and Sequences

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is:
    Show that an [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] an [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 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. jcsd
  3. Apr 4, 2012 #2


    User Avatar
    Science Advisor

    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]?
  4. Apr 5, 2012 #3
    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...
  5. Apr 5, 2012 #4
    Then your homework doesn't make much sense...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook