Puzzles & Games Proof that 2 = 1 - solved

Discussion in 'Puzzles & Games' started by kiwirobin, Feb 14, 2005.

  1. kiwirobin

    kiwirobin Premium Member

    A Proof That 2 = 1

    Given
    (1) X = Y

    Multiply both sides by X
    (2) X^2 = XY

    Subtract Y^2 from both sides
    (3) X^2 - Y^2 = XY - Y^2

    Factor both sides
    (4) (X+Y)(X-Y) = Y(X-Y)

    Cancel out common factors
    (5) (X+Y) = Y

    Substitute in from line (1)
    (6) Y+Y = Y

    Collect the Y's
    (7) 2Y = Y

    Divide both sides by Y
    (8) 2 = 1


    Q: What's wrong with this 'proof'?

    [Edited on 2-16-2005 by kiwirobin]
     
  2. junior_smith

    junior_smith Premium Member

    whya re you adding and subtractnig variables because i could do that with anything and make it equal to any number
     
  3. kiwirobin

    kiwirobin Premium Member

    Ok the j_s then answer the question.
    Show me the flaw in the proof!!:p
     
  4. Icewolf

    Icewolf Premium Member

    The only way that this will work out is if,
    x = y = 0

    Which leads to the point that zero obejects cannot be divided into zero groups. (if you want a more detailed answer I can give you it)
     
  5. kiwirobin

    kiwirobin Premium Member

    This is also correct ice but the challange was to solve this problem.

    Q: What's wrong with -THIS- 'proof'?

    Where is the application that is not correct.
     
  6. Icewolf

    Icewolf Premium Member

    Part 5, cancel out means divide, if we say
    x = 0
    y = 0
    therefore x - y = 0

    therefore you are dividing by 0 which is not allowed

    [Edited on 16-2-2005 by Icewolf]
     
  7. kiwirobin

    kiwirobin Premium Member

    That's it ice:up::up::up:
    Took me ages to find it, funny how my brain can only vocus on one thing sometimes exclueding the obvious.
    For a while there I was starting to believe it...:mnky:

    anyway, well done...
    here's the breakdown for those interested...

    2 = 1: Solution
    'Cancelling' the common factors from line (4) to (5) means dividing by the factor (X-Y). Since X=Y, this is a division by 0, the results of which are undefined.

    (1) X = Y Given
    (2) X^2 = XY Multiply both sides by X
    (3) X^2 - Y^2 = XY - Y^2 Subtract Y^2 from both sides
    (4) (X+Y)(X-Y) = Y(X-Y) Factor both sides
    (5) (X+Y) = Y Cancel out common factors
    (6) Y+Y = Y Substitute in from line (1)
    (7) 2Y = Y Collect the Y's
    (8) 2 = 1 Divide both sides by Y