Results 1 to 3 of 3

Math Help - Real analysis - set theory

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Real analysis - set theory

    Hola seņores

    I'm just hoping that someone can verify what i write next,

    the set R^{+} = \{ x \in R : x > 0 }
    is closed because the epsilon-neighbourhood around the lower limit, 0, will intersect elements in R-positive

    is that adequate reasoning?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Sep 2009
    From
    Johannesburg, South Africa
    Posts
    71
    Quote Originally Posted by walleye View Post
    Hola seņores

    I'm just hoping that someone can verify what i write next,

    the set R^{+} = \{ x \in R : x > 0 }
    is closed because the epsilon-neighbourhood around the lower limit, 0, will intersect elements in R-positive

    is that adequate reasoning?
    R^{+} is closed if and only if R^{+} contains all its adherent points. x_{0} is an adherent point of R^{+} if for every radius r>0, the ball B_r(x_0), that is, { {x \in R^{+} :  |x-x_0|<r} } has a non-empty intersection with R^{+}. Is 0 an adherent point and does R^{+} contains 0?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by walleye View Post
    Hola seņores

    I'm just hoping that someone can verify what i write next,

    the set R^{+} = \{ x \in R : x > 0 }
    is closed because the epsilon-neighbourhood around the lower limit, 0, will intersect elements in R-positive

    is that adequate reasoning?
    Quote Originally Posted by bram kierkels View Post
    R^{+} is closed if and only if R^{+} contains all its adherent points. x_{0} is an adherent point of R^{+} if for every radius r>0, the ball B_r(x_0), that is, { {x \in R^{+} :  |x-x_0|<r} } has a non-empty intersection with R^{+}. Is 0 an adherent point and does R^{+} contains 0?
    Well, I guess that it depends on what topology \mathbb{R} has. If it's the usual topology then the above user has the correct reasoning.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Real analysis help please
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 19th 2009, 06:31 PM
  2. real analysis
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: August 21st 2009, 02:26 PM
  3. Real Analysis Help!!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 6th 2008, 07:38 PM
  4. Real analysis
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 27th 2008, 11:58 AM
  5. Need Some Help with Real Analysis
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 19th 2006, 02:31 PM

Search Tags


/mathhelpforum @mathhelpforum