1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Is this correct(proof)?

  1. Oct 17, 2008 #1
    I figured it out.
    Last edited: Oct 17, 2008
  2. jcsd
  3. Oct 17, 2008 #2
    If x is any real number? I'd choose a number more interesting than [tex]x=\pi[/tex]. Remember that the claim employs "either/or", so if both [tex]\pi - x[/tex] and [tex]x+\pi[/tex] are irrational the claim is false.
  4. Oct 17, 2008 #3
    So the proof is incorrect because the statement is false? How do you know its an exclusive or?
  5. Oct 17, 2008 #4
    Yes. Give a counterexample to disprove the claim. It's an exclusive or because that's the language you use when it's an exclusive or. EITHER x-pi is irrational OR x+pi is irrational is what the claim is for any real x, so if they're both irrational then that isn't "either", that's "both".
  6. Oct 17, 2008 #5
    If you changed it to either A... or...B, or both, then the statement and proof would be true?
  7. Oct 17, 2008 #6
    well strictly speaking just dropping "either" would work, but nobody ever uses "or" to mean logical or. But yes what you say is right.

    Edit: Yeah Cristo is right I had totally forgotten about any "proof" by the time I wrote this.
    Last edited: Oct 17, 2008
  8. Oct 17, 2008 #7


    User Avatar
    Staff Emeritus
    Science Advisor

    The proof is incorrect on a more fundamental level: namely, it is not a proof. It gives one example, but it is claimed that this holds for any x, hence a proof must show this. Remember, you cannot prove a general case by one example.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook