Results 1 to 2 of 2

Math Help - Help with Analysis please :)

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    25

    Question Help with Analysis please :)

    I'm really quite distraught on two particular questions... I have attempted them, but I am new at proofs and help / ideas as to how to start these two proofs would be greatly appreciated! Thank you in advance!!

    Prove that the only set in R1 which is open and closed are the empty set and R1 itself.
    Given a set S in Rn with the property that for any x that is an element of S there is an n-ball B(x) such that B(x)S is countable. Prove that S is countable.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,577
    Thanks
    1418
    Quote Originally Posted by Majialin View Post
    I'm really quite distraught on two particular questions... I have attempted them, but I am new at proofs and help / ideas as to how to start these two proofs would be greatly appreciated! Thank you in advance!!

    Prove that the only set in R1 which is open and closed are the empty set and R1 itself.
    There are different ways of defining "open" and "closed" set. The correct way of proving this depends on what definitions you are using.

    One definition is that a set is "open" if it contains none of its "boundary" points and "closed if it contains all of its "boundary" points. If that is the definition you have then being "open" and "closed" means that "all" and "none" of its boundary points must be the same. What are the boundary points of the empty set? What about R? Can you show that any other set must have at least one boundary point?

    Given a set S in Rn with the property that for any x that is an element of S there is an n-ball B(x) such that B(x)S is countable. Prove that S is countable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. analysis help
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 16th 2010, 04:30 PM
  2. analysis!!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 9th 2009, 12:52 PM
  3. analysis 4.1.1
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 07:57 PM
  4. analysis 4.1.3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 07:51 PM
  5. Please help with a bit of analysis!!!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 16th 2008, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum