Results 1 to 7 of 7

Math Help - dedekind sets

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    6

    dedekind sets

    How do you prove sqrt(2) > 1 using dedekind sets
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by l888l888l888 View Post
    How do you prove sqrt(2) > 1 using dedekind sets
    I must wonder if by "using dedekind sets" you mean Dedekind cuts?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    6
    yes my professor uses both in his lecture. sorry
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,444
    Thanks
    1863
    Quote Originally Posted by l888l888l888 View Post
    How do you prove sqrt(2) > 1 using dedekind sets
    What is the definition of "1" as a Dedekind cut? What is the definition of \sqrt{2} as a Dedekind cut? What does ">" mean for Dedekind cuts?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    6
    for sqrt(2) it is defined as :{x belongs to Q: (X^2) < 2 V X < 0}
    for 1 it is defined as : {x belong to Q: X<1}
    tO PROVE > you have to prove {x belongs to Q: X<1} IS A SUBSST OF
    {X belongs to Q: (x^2) < 2 V X < 0}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,444
    Thanks
    1863
    Quote Originally Posted by l888l888l888 View Post
    for sqrt(2) it is defined as :{x belongs to Q: (X^2) < 2 V X < 0}
    for 1 it is defined as : {x belong to Q: X<1}
    tO PROVE > you have to prove {x belongs to Q: X<1} IS A SUBSST OF
    {X belongs to Q: (x^2) < 2 V X < 0}
    And that is straight forward, isn't it? If x is in the Dedekind cut "1" then either x< 0 or 0\le x< 1. In the first case, x in the Dedekind cut " \sqrt{2}" because that cut includes "X< 0". In the second case, 0\le x< 1, what can you say about x^2?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    6
    x^2 is also between 0 and 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 2nd 2011, 03:26 AM
  2. e as a Dedekind cut
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 14th 2011, 09:38 PM
  3. Dedekind Cut
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 22nd 2010, 08:03 AM
  4. Dedekind Domain
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 26th 2008, 12:39 AM
  5. Dedekind Cuts?
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: October 31st 2007, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum