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!

-1 = 1?

  1. Apr 3, 2009 #1
    Hi all. I found this "proof" and was just wondering if there is an error in it or not, because I couldn't find it. Any ideas?

    -1=1 ?
  2. jcsd
  3. Apr 3, 2009 #2

    The transition between these two steps is invalid. There is no reason you would be allowed to do this.

    There is a basic property of the square root function that sqrt(a)*sqrt(b)=sqrt(a*b) where a and b are positive, but -1/1 isn't positive so we don't get to use that here.

    I've actually seen this one before a page promoting "Time Cube" theory!
  4. Apr 3, 2009 #3
    The problem comes from writing simple "sqrt" functions rather than "+/-sqrt". IOW, whenever you take the square root, you have to take into consideration that there are two square roots of any complex number, which differ by a factor of -1. Deciding which roots to take to maintain an equality often requires working through exactly the kind of computation you have shown.

    I would have looked at the second line in your "proof" and decide which sign each sqrt should have. To do that I would go through pretty much the proof you have, and when I got "-1=1", I would say, "Oh - that's not it - I guess the two sqrts have to have opposite signs to maintain the equality."

    I know that looks circular, but it's really how you decide which root to take. It might be clearer with pure real numbers:

    (-2)^2 = (2)^2
    sqrt((-2)^2) = sqrt((2)^2)
    -2 = 2

    oops ... should have had a minus sign in line 2!
  5. Apr 3, 2009 #4
    Just to add this wasn't my proof and I knew it wasn't true. I just couldn't find the mistake. Thanks guys.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook