Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math Proof

  1. Jun 15, 2015 #1

    wfc

    User Avatar

    How could you prove that if x*y ≠ -1, then x/y ≠ -1?

    x*y ≠ -1 → x ≠ -1/y

    I'm not sure where to go after that.
     
  2. jcsd
  3. Jun 15, 2015 #2

    wabbit

    User Avatar
    Gold Member

    You don't prove it, because it isn't true. Can you find a couterexample ?
     
  4. Jun 15, 2015 #3
    Assuming it were true (which it isn't), the best way would be to do contraposition. It would then suffices to show that ##x/y = -1## implies ##xy = -1##.
     
  5. Jun 15, 2015 #4

    wfc

    User Avatar

    Can you explain why it isn't true? I'm still confused.

    And where you say x/y = -1, then xy = -1, I can't come up with an example where that would work?
     
  6. Jun 15, 2015 #5
    If you can't come up with an example where that would work, then that means it's false.
     
  7. Jun 15, 2015 #6

    wabbit

    User Avatar
    Gold Member

    What you need to find is an example of ## x,y ## such that ## x/y=-1 ## and ## xy\neq -1 ## .

    Once you've done that you've proved that your initial statement ## (xy\neq -1\Rightarrow x/y\neq -1 )## is false
     
  8. Jun 16, 2015 #7
    if x ≠ -1/y then (-1/y)/y ≠ -1 -> here we go that -1 ≠ -1 so its not true
     
  9. Jun 16, 2015 #8

    wabbit

    User Avatar
    Gold Member

    No, this does not follow at all.
     
    Last edited: Jun 16, 2015
  10. Jun 16, 2015 #9

    Svein

    User Avatar
    Science Advisor

    Counterexample:

    Put x = -2, y=2. Then x⋅y = -4 (which is not -1) and x/y = -1.
     
  11. Jun 16, 2015 #10

    wabbit

    User Avatar
    Gold Member

    You don't leave any stone unturned :)
     
  12. Jun 17, 2015 #11

    Svein

    User Avatar
    Science Advisor

    I am a mathematician. I have to turn them.
     
  13. Jun 21, 2015 #12
    It would probably be easiest to first attempt to find a counterexample. (it's pretty easy, if you let x and y be numbers with the same absolute value but opposite signs)

    If that for some reason turns out fruitless, you can attempt a proof. Contradiction is probably the easiest (because it's really saying the same thing as finding a specific counterexample!).

    Instead of proving that for every x and y in the universe, xy ≠ -1 ⇒ x/y ≠ -1, the negated sentence is a bit easier to bite into: xy≠ -1 ∧ x/y = -1. Prove that two numbers x and y can't exist to make this true.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...