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)