Results 1 to 6 of 6

Math Help - completion of set in metrix spaces

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    70

    completion of set in metrix spaces

    Hi, can one help me please;

    completion of set in metrix  spaces-untitled.jpg

    For S=(0,1)

    We know the Cauchy sequences Xn=1/n converges to zero which is not in the set
    and Xn=1/n+1 converges to one which is also not in the set

    so S=[0,1].

    For S= [0,1] n {Rational numbers}

    is it just the set of all Real numbers.

    For S={1/k:k=1,2,3,...}

    Not really to sure about this one

    Many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1
    What does completion mean?
    Is that what the rest of us know as closure?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    70
    Hi, yes it is closure. so that the metric can be complete.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1
    a) & b) ~\overline{S}=[0,1]

    c) ~\overline{S}=S\cup \{0\}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2009
    Posts
    70
    Quote Originally Posted by Plato View Post
    a) & b) ~\overline{S}=[0,1]

    c) ~\overline{S}=S\cup \{0\}
    For B) if one took the set Xn= x/2+1/x then this in the set S= [0,1] n {Rational numbers} and the sequence converges to
    square root 2 but that not within the set [0,1].

    SO how can For B) b) ~\overline{S}=[0,1]
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by nerdo View Post
    For B) if one took the set Xn= x/2+1/x then this in the set S= [0,1] n {Rational numbers} and the sequence converges to
    square root 2 but that not within the set [0,1].

    SO how can For B) b) ~\overline{S}=[0,1]
    The fact that \overline{\mathbb{Q}\cap[0,1]}=[0,1] follows since \mathbb{Q} is dense in \mathbb{R} and the fact that \overline{\mathbb{Q}\cap [0,1]}\supseteq\overline{\mathbb{Q}}\cap\overline{[0,1]}=\mathbb{R}\cap[0,1]=[0,1]. But, since \mathbb{Q}\cap[0,1]\subseteq[0,1] we have that \overline{\mathbb{Q}\cap[0,1]}\subseteq\overline{[0,1]}=[0,1] from where the conclusion follows.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Determine Components of Metrix Tensor Relative to a Basis
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: September 7th 2011, 03:14 PM
  2. completion of space
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 20th 2011, 10:10 AM
  3. Completion of the Hyperreal numbers?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: February 19th 2011, 04:09 AM
  4. Probability of completion.
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: January 3rd 2011, 07:01 PM
  5. skew-symmetric metrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 24th 2010, 04:18 AM

Search Tags


/mathhelpforum @mathhelpforum