Results 1 to 2 of 2

Math Help - Please check my proof

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    22

    Please check my proof

    Prove: For all a,b in R,
    if a is rational,
    a+b is irrational
    then b is irrational

    PF
    Let a be rational, and b be irrational. Then a=c/d for some c,d and there is no e,f such that e/f=b.
    Assume a+b is rational. Then there exists a j,k, such that j/k=a+b.
    Then b=(a+b)-a = j/k-c/d = (jd - ck)/ dk.
    Hence e= dj-ck and f= dk.
    Contradiction
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    677
    Quote Originally Posted by jujab View Post
    Prove: For all a,b in R,
    if a is rational,
    a+b is irrational
    then b is irrational

    PF
    Let a be rational, and b be irrational. Then a=c/d for some c,d and there is no e,f such that e/f=b.
    Assume a+b is rational. Then there exists a j,k, such that j/k=a+b.
    Then b=(a+b)-a = j/k-c/d = (jd - ck)/ dk.
    Hence e= dj-ck and f= dk.
    Contradiction
    Hi - All ok. But what you have proved is
    If a is rational, b is irrational => a+b is irrational.

    Nevermind, tweak your proof a little, that's all
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof check please: Two DFA's
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 28th 2011, 09:37 PM
  2. [SOLVED] check my proof f(phi) = phi
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: October 15th 2010, 08:54 AM
  3. Set Proof check
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: October 8th 2009, 03:15 PM
  4. Check my proof
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 9th 2008, 10:34 PM
  5. Check this proof.
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 4th 2006, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum