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!

Definition of a Limit.

  1. Oct 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Given a function [tex]f:R\rightarrow R[/tex] and a number L,write down a definition of the statement


    3. The attempt at a solution

    Is it just [tex]\lim_{x\rightarrow-\infty}f(x)=\lim_{x\rightarrow\infty}f(-x)[/tex] ?

    and definition is
    for [tex]\forall \epsilon>0[/tex] [tex]\exists N[/tex] such that [tex]\forall n>N[/tex]
    we have [tex]|f(-x)-L|<\epsilon[/tex]
  2. jcsd
  3. Oct 21, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    assuming by n you mean x, then yes, this looks like a good dfn, although the usual dfn is that "for all e>0, there is an N<0 such that x<N ==>|f(x)-L|<e"
  4. Oct 21, 2007 #3
  5. Oct 21, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    A more "standard" definition of
    would be:

    "Given [itex]\epsilon> 0[/itex], there exist N such that if x< N, then [itex]|f(x)-L|<\epsilon[/itex]."

    Notice that in neither this definition nor your definition is N required to be an integer.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Definition of a Limit.
  1. Definition of Limit (Replies: 2)

  2. Definition of Limit (Replies: 3)

  3. Definition of Limit (Replies: 2)

  4. Definition of a limit (Replies: 3)

  5. Definition of a Limit (Replies: 1)