Mathmatical paradox?

Discussion in 'Physics & Math' started by speeding electron, Nov 8, 2003.

  1. speeding electron Registered Member

    Messages:
    10
    Take the equation:

    x +1 = 0 (1)

    Now simple algebra would tell us that the solution is:

    x = -1 (2)

    But what if we divided each side of (1) by (x + 1)? This would lead us to the conclusion that 1=0 . If one was teach someone algebra and they did this, one would probably say to them that it was necessary to take our added constast (here = 1) to the other side of the equation so that we don't have such an awkward number as 0 on either side of the equation, a number which will still equal itself when divided by anything. But why does this operation leave us with such a paradoxical result result? There is probably a perfect good mathmatical reason behind this that when explained will make me look a fool, but I feel the need to address it, seeing as equating expressions to zero is so common.
     
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  3. lethe Registered Senior Member

    Messages:
    2,009
    you cannot divide by zero. x+1 is zero, by hypothesis, so you cannot divide by it.

    dividing by zero often leads to paradoxical results, as you are discovering. that is why it is not allowed.

    the math police will be knocking on your door soon. its been nice knowing you.
     
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  5. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    The expression:

    1 = 0 / (x+1)

    is perfectly valid, unless x = -1. In the case where x = -1, the expression on the right hand side is indeterminate.

    So, if you take the equation:

    x + 1 = 0

    and divide both sides by (x+1), you must realise that the resulting equation is only valid for x not equal to -1.

    It is a common mistake in mathematics to forget to check for division by zero. It leads to all kinds of incorrect "proofs", such as this one:

    Let x be arbitrary, and y = x

    Then square both sides:
    y<sup>2</sup> = x<sup>2</sup>

    Subtract x<sup>2</sup> from both sides:
    y<sup>2</sup> - x<sup>2</sup> = x<sup>2</sup> - x<sup>2</sup>

    Factorise LHS and simplify RHS:

    (y - x)(y + x) = 0

    Divide both sides by (y - x):

    y + x = 0

    But y = x, so:

    x + x = 0

    2x = 0

    x = 0

    The initial assumption was that x is arbitrary, so this proves that all numbers are equal to zero.
     
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  7. John Connellan Valued Senior Member

    Messages:
    3,636
    Doesn't matter if theres a constant or not !

    Just let x = 0 (without the 1)

    divide both sides by x

    1 = 0

    Surprise!!!!!!!
     
  8. Mephura Applesauce, bitch... Valued Senior Member

    Messages:
    1,065
    x=0
    divide both sides by x and you get 1=0?
    nope.

    you get 0/0=0/0

    x=0

    remember?

    it's undefined..
    (though tends towards infinity)
     
  9. John Connellan Valued Senior Member

    Messages:
    3,636
    Very true, but I was just demonstrating how simple algebraic rules break down when dealing with zero's!
     
  10. Mephura Applesauce, bitch... Valued Senior Member

    Messages:
    1,065
    If you ask me, it's all zero's fault. I think we should just ban the use of zero from all math..
    ok, kidding.
    Still, I would like to see something done about it. I understand why it is undefined, but I still don't like that big gaping hole sitting in the middle of the neat little package they sell you at such a young age. It's like buying a new keyboard and having a big red button on it that says "do not push". It's annoying.

    We must find rules for that little beast, or it will run wild with all of mathematics! You wouldn't want that to happen would you?

    Rules are what zero needs. Yes! Zero and all his little trouble making friends. i, that irratoinal gang that is running around, all of them. They are nothing but a bunch of trouble makers.
     
  11. hlreed Registered Senior Member

    Messages:
    245
    The problem is not with 0. It is with division. You simply cannot divide everything. Its against the law.
     

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