Results 1 to 4 of 4

Math Help - Bounded, Continuous and Closed Functions

  1. #1
    Member Ranger SVO's Avatar
    Joined
    Apr 2006
    From
    Abilene Tx
    Posts
    90

    Bounded, Continuous and Closed Functions

    I need a clearer definition of a bounded, continuous and closed function. The lecture Wendnsday wasnt real clear.

    What I know, a function is bounded if it lives between two horizontal lines. An example would be the function f(x)=sin(x). Its bounded between 1 and -1.
    I also know that its continuous, but why is it closed? What does that mean?

    The function f(x)=1/x D=(0,1) is bounded and continuous on its Domain, is it closed?

    A more clear explination would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member tukeywilliams's Avatar
    Joined
    Mar 2007
    Posts
    307
    A closed set contains all of its limit points. An open set does not. Basically, closed intervals are closed, and open intervals are open. So  (0,1) is open.  \sin x is closed, because it contains its boundary. See this

    A closed and bounded set is said to be compact.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Ranger SVO View Post
    I need a clearer definition of a bounded, continuous and closed function. The lecture Wendnsday wasnt real clear.

    What I know, a function is bounded if it lives between two horizontal lines. An example would be the function f(x)=sin(x). Its bounded between 1 and -1.
    I also know that its continuous, but why is it closed? What does that mean?

    The function f(x)=1/x D=(0,1) is bounded and continuous on its Domain, is it closed?

    A more clear explination would be greatly appreciated.
    A "boundary point" is like an endpoint so [1,2] has two boundary points 1 and 2. Also (1,2) has two 1 and 2 boundary points. An interval (or a set) which contains its boundary points is said to be "closed" so [1,2] is closed. While (1,2) is not closed. An interval (or a set) which contains none of its bounday points is "open" so (1,2) is open. Note, [1,2) is neither open nor closed.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Ranger SVO's Avatar
    Joined
    Apr 2006
    From
    Abilene Tx
    Posts
    90
    Thats the explination that I needed, thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. continuous bounded functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 22nd 2010, 07:53 PM
  2. continuous function on a closed and bounded set
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 10th 2009, 03:58 PM
  3. Replies: 1
    Last Post: February 7th 2009, 07:38 AM
  4. Replies: 1
    Last Post: October 12th 2008, 11:22 AM
  5. continuous on closed and bounded interval
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 13th 2007, 09:59 AM

Search Tags


/mathhelpforum @mathhelpforum