Results 1 to 4 of 4

Math Help - clarification

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    clarification

    i was just wondering which is correct:

    a function f is defined on an interval I is contonuous if lim as x->c for f(x) is f(c) for all x in I or for all c in I.

    i thought it should be the former but the book that im reading states that its the latter.

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    It is the latter.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Aug 2009
    Posts
    639
    thanks for the clarification..but may i know why, if for this case, it is the latter then for this case:
    a function f is cont at c if every seq of points x_n in I such that lim as n->infinity for x_n is c if the lim n->inifinity f(x_n) is f(c).
    in this case, we are talking about x_n in I and not for all c in I.

    i hope im making sense
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alexandrabel90 View Post
    thanks for the clarification..but may i know why, if for this case, it is the latter then for this case:
    a function f is cont at c if every seq of points x_n in I such that lim as n->infinity for x_n is c if the lim n->inifinity f(x_n) is f(c).
    in this case, we are talking about x_n in I and not for all c in I.

    i hope im making sense
    Think about what you're saying in a simpler sense. This x is a "dummy" variable, in the same sense as the x in \displaystyle \int_a^b f(x)\text{ }dx. What's really fixed is the c\in I. Think about your definition you gave in terms of sequences. A function is continuous on I if at every \mathbf{c}\in I that's true. No?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Clarification
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: August 20th 2010, 12:48 PM
  2. Need some clarification
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 28th 2010, 01:54 AM
  3. clarification
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 28th 2010, 05:17 AM
  4. clarification
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: March 17th 2010, 04:24 PM
  5. clarification
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 13th 2010, 01:07 PM

Search Tags


/mathhelpforum @mathhelpforum