Results 1 to 4 of 4

Math Help - Rational Number - Question

  1. #1
    Super Member
    Joined
    Apr 2009
    Posts
    677

    Rational Number - Question

    Let p be a rational number.
    p^2 < 2

    Find another rational number q, such that q>p AND q^2 < 2

    [I am stuck on Rudin pg 1 . I am struggling to find an explanation as how would anyone get (2p+2)/(p+2). It works but I couldn't have imagined it - so is there a way we can do it systematically?]

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,706
    Thanks
    1637
    Awards
    1
    Quote Originally Posted by aman_cc View Post
    Let p be a rational number. p^2 < 2
    Find another rational number q, such that q>p AND q^2 < 2
    I am struggling to find an explanation as how would anyone get (2p+2)/(p+2). It works but I couldn't have imagined it - so is there a way we can do it systematically?]
    I answered this very question several times.
    The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
    Someone, most likely before Rudin, found that one simply worked.
    I have seen several others. Bevin Youse uses \frac{4p}{p^2+2} which also works.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Apr 2009
    Posts
    677
    Quote Originally Posted by Plato View Post
    I answered this very question several times.
    The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
    Someone, most likely before Rudin, found that one simply worked.
    I have seen several others. Bevin Youse uses \frac{4p}{p^2+2} which also works.
    Thanks. Good to know people have struggled before me as well. I was like little disappointed - It was pg 1 of Rudin after all !!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Apr 2009
    Posts
    677
    Quote Originally Posted by Plato View Post
    I answered this very question several times.
    The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
    Someone, most likely before Rudin, found that one simply worked.
    I have seen several others. Bevin Youse uses \frac{4p}{p^2+2} which also works.
    @Plato - I seem to have hit on a way it can be 'worked' out. This is based on a proof in Bartle book.

    We know p^2<2
    we need another rational x>0 such that (p+x)^2<2
    x(x+2p)<2-p^2
    Note x<2 => Any x<\frac{2-p^2}{2+2p} will do.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Is this a rational number?
    Posted in the Algebra Forum
    Replies: 7
    Last Post: October 6th 2011, 08:40 AM
  2. Replies: 4
    Last Post: April 28th 2011, 06:20 AM
  3. Is the following a rational number?
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: December 6th 2009, 01:38 PM
  4. Replies: 5
    Last Post: October 7th 2008, 12:55 PM
  5. Rational Number
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 30th 2006, 04:43 PM

Search Tags


/mathhelpforum @mathhelpforum