Results 1 to 2 of 2

Math Help - definition of a limit

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    166

    definition of a limit

    Suppose g:[0,\infty)\rightarrow\mathbb{R} and L\in[-\infty,\infty]. Prove that lim_{t\rightarrow\infty}g(t)=L \iff for every increasing sequence (a_n) in [0,\infty), if a_n\rightarrow\infty, then g(a_n) \rightarrow L.

    I'm trying to prove [<==] when L=\infty by contradiction. But not sure about the definition:
    lim_{t\rightarrow\infty}g(t)=\infty means that \forall M>0 , there is x\in[0,\infty) such that \forall t>x, g(t)>M. Is this the correct definition?
    So if lim_{t\rightarrow\infty}g(t)\not=\infty, then there exists  M>0 such that \forall x\in[0,\infty) there exists t>x such that  g(t) \leq M. Right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    Hello.

    Your definition seems to be correct.

    Now, you can try for a contradiction/contrapositive by constructing an increasing sequence \{a_n\} which diverges to infinity but \{g(a_n)\} does not.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit definition
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 9th 2010, 09:46 AM
  2. Replies: 1
    Last Post: February 5th 2010, 04:33 AM
  3. Definition of Limit
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 7th 2009, 04:09 PM
  4. use LIMIT definition
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 12th 2009, 11:06 PM
  5. Replies: 15
    Last Post: November 4th 2007, 08:21 PM

Search Tags


/mathhelpforum @mathhelpforum