1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Increasing Sequence

  1. Nov 5, 2005 #1
    Suppose f:[a,b)->R is such that lim(x->b-)=+inf. Prove that there exists an increasing sequence {x_n} in (a,b) such that f(x_n)>n for all n.

    I don't know where to start. It would be easy if I can prove that f is strictly increasing after some point. f might not be continuous so I can't simply look for all f(x) in the form x^2 or something... Too many possibilities. Any pointers will be helpful!
     
    Last edited by a moderator: Nov 5, 2005
  2. jcsd
  3. Nov 5, 2005 #2

    benorin

    User Avatar
    Homework Helper

    What do you have for a definition of lim(x->b-)=+inf ? This will tell you where to start.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?