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A little problem

  1. Sep 5, 2009 #1

    PrincePhoenix

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    Why is 2 = 3 over here?

    Suppose 2=3

    Then subtract 5/2 from both sides.
    2 - 5/2 = 3 - 5/2
    4-5/2 = 6-5/2
    -1/2 = 1/2

    Take square root
    (-1/2)2 = (1/2)2
    1/4 = 1/4

    What's wrong? why is it proved that 2 = 3?
     
    Last edited: Sep 5, 2009
  2. jcsd
  3. Sep 5, 2009 #2

    Doc Al

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    You didn't prove anything. Note that when you square both sides you effectively multiply the sides by different numbers.
     
  4. Sep 5, 2009 #3
    Maybe it is because I am not fully awake yet, but I do not follow your arithmetic.

    2 - 5/4 = 3/4 not -1/2
    3 - 5/4 = 7/4 not 1/2
     
  5. Sep 5, 2009 #4

    PrincePhoenix

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    So you mean that taking square was wrong? I thought I did everything on both sides of the equation. I mean which step is incorrect?
     
  6. Sep 5, 2009 #5

    PrincePhoenix

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    I corrected the mistake. Check again.
     
  7. Sep 5, 2009 #6

    jgens

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    When you square an equation, you run the risk of creating extraneous roots. For example, [itex]-2^2 = 2^2 = 4[/itex] but this does not prove that [itex]-2 = 2[/itex]. Also, another mistake you made is assuming what you're trying to prove. To have a correct proof you would need to begin with the equaltiy [itex]1/4 = 1/4[/itex] and proceed to show that [itex]2 = 3[/itex] (which you can't do).

    Edit: Just so it's clear, the biggest fallacy in your "proof" was the assumption that [itex]2 = 3[/itex]. You can't assume what you're trying to prove.
     
  8. Sep 5, 2009 #7

    jgens

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    To absolutely clear, here's why you can't assume what you're proving . . .

    Let [itex]a,b \in \mathbb{R}[/itex] and suppose that [itex]a = b[/itex]. Then clearly we have that [itex]0*a = 0*b = 0[/itex]. Hence, if [itex]a[/itex] and [itex]b[/itex] are any two real numbers, then they are equal to each other (using your same logic). A correct proof would need to start at the equality [itex]0 = 0[/itex] and work from there (which is impossible).
     
  9. Sep 5, 2009 #8

    PrincePhoenix

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    Thanks for the answers. I didn't want to PROVE anything here. This was just shown to me by a friend and I just wanted to know what was wrong.
     
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