Results 1 to 5 of 5

Math Help - question on continuity of functions

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    22

    question on continuity of functions

    Okay, so in general, if I wanted to do a proof to show that some function f(x) is continuous for all x, how do i do that? I mean, general proofs of continuity are easy, but how do you prove it to be continuous for all x in a set?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1607
    Awards
    1
    Quote Originally Posted by jmoney90 View Post
    Okay, so in general, if I wanted to do a proof to show that some function f(x) is continuous for all x, how do i do that? I mean, general proofs of continuity are easy, but how do you prove it to be continuous for all x in a set?
    Choose any point in the set, say c.
    Then by showing that the function f is continuous at c suffices to show that f is continuous on the set.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    22
    Quote Originally Posted by Plato View Post
    Choose any point in the set, say c.
    Then by showing that the function f is continuous at c suffices to show that f is continuous on the set.
    Okay, thanks. So just to clarify, basically you prove it by being vague and general, and not picking specific values?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1607
    Awards
    1
    Quote Originally Posted by jmoney90 View Post
    So just to clarify, basically you prove it by being vague and general, and not picking specific values?
    Why do you think that there is anything vague about that method?

    You suppose that c\in S and show that f is continious at c.
    There is absolutely nothing vague about that.

    Maybe you don't understand the definition of continuity. Is that it?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    22
    Quote Originally Posted by Plato View Post
    Why do you think that there is anything vague about that method?

    You suppose that c\in S and show that f is continious at c.
    There is absolutely nothing vague about that.

    Maybe you don't understand the definition of continuity. Is that it?
    I guess general was more the word I was looking for. I understand the idea behind continuity: the limit as x approaches some point is the same as that function at some value, and alos how to formally work the definition. The book didn't give any examples of a prooof in which you'd prove continuity of a function in general.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Functions of two variables continuity question
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 15th 2010, 11:28 AM
  2. more continuity of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 9th 2009, 12:26 AM
  3. Continuity of Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 1st 2008, 02:14 PM
  4. Continuity of Functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 17th 2008, 11:30 AM
  5. Continuity Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 11th 2007, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum