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: Spivak 2=1 Proof fallacy

  1. Dec 16, 2009 #1
    Hi, I've gotten Spivak's calculus and I have a question on the second proof in the first chapter

    What is wrong with the following "proof"?

    suppose x=y

    1. x² = xy

    2. x² - y²= xy - y²

    3. (x + y)(x - y)=y(x - y)

    4. x + y=y

    5. 2y = y

    6. 2 = 1

    I just want to clarify that the error is in the transition from step three to step four as subtracting both sides by (x - y) is to subtract by zero as if x=y then x -y = 0.

    Step two is also saying that 0 = 0.
  2. jcsd
  3. Dec 16, 2009 #2


    Staff: Mentor

    No, that's not it at all. You have correctly identified the step that is incorrect, but not the reason. What they have done in going from step 3 to step 4 is to divide by x - y, not subtract x - y. There is never a problem subtracting the same amount from both sides of an equation, but you can run into problems by dividing both sides by a quantity that happens to be zero.
  4. Dec 16, 2009 #3
    Sorry I meant divide, misuse of language. Good to hear I got it, Spivak doesn't seem so difficult now :tongue:

    - foolish last words
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook