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X-x = 0

  1. Oct 23, 2009 #1
    i have been wondering about something and i can think of a way to prove myself wrong so... here it is:

    if X= the square root of 1

    the square root of 1 = 1 or -1

    the square root of 1 = the square root of 1 these are true yes?

    therefore 1 = -1

    X-X = 2 because 1--1=2
    X-X = -2 because -1-1=2
    X-X = 0 because 1-1=0
     
  2. jcsd
  3. Oct 23, 2009 #2

    DaveC426913

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    Re: x-x=0?

    You cannot conclude that 1 = -1 from your initial arguments. It does not follow.
     
  4. Oct 23, 2009 #3

    arildno

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    Re: x-x=0?

    Suppose you have the equation:
    [tex]x^{2}=1[/tex]

    This can be rewritten as:
    [tex](x-1)*(x+1)=0[/tex]
    and x can then either be 1 or -1.

    It does not follow that
    1=-1
     
  5. Oct 23, 2009 #4
    Re: x-x=0?

    X=X
    the square root of 1 = the square root of 1
    the square root of 1 = 1
    the square root of 1 = -1
    therefore x can be 1 or -1
    therefore x-x=2 or -2 or 0 im trying to find an explanation as to why its wrong.. i know its wrong but i dont know why... it seems logical and illogical at the same time
     
  6. Oct 23, 2009 #5

    DaveC426913

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    Re: x-x=0?

    X can be 1 OR -1. Not BOTH at the same time - or not one then the other within the same equation.



    Walk it through.

    root(x) can be 1 or -1.
    Now pick one.
    Now put it into x-x=0. Paradox goes away.
     
  7. Oct 23, 2009 #6

    JasonRox

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    Re: x-x=0?

    Above!
     
  8. Oct 23, 2009 #7
    Re: x-x=0?

    your not explaining your telling, sorry for not taking your word as gospel but feckin prove it
     
  9. Oct 23, 2009 #8

    DaveC426913

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    Re: x-x=0?

    Are you seriously copping a 'tude?

    You're the one who doesn't understand. It has been proven.
    Ths onus is on you to lay down math that is valid. It is not valid.
    The fact that you don't follow it does not give you cause to be rude.

    I'll try again.

    X can be 1 or -1.
    That's an OR; it is not an AND. X cannot be 1 AND -1.

    When you write your equation x-x=0
    and then substitute for x, you write (1)-(-1)=0. You cannot do this.
    X has one value.
     
  10. Oct 23, 2009 #9
    Re: x-x=0?

    i just want an explanation ... it doesnt make sense and im sorry ive been thinking about it for ages and you just say no with no evidence
     
  11. Oct 23, 2009 #10
    Re: x-x=0?

    why cant they be used independently?
     
  12. Oct 23, 2009 #11
    Re: x-x=0?

    surely 1 equation cant give 2 answers
    X must have 2 values in this case?
     
  13. Oct 23, 2009 #12
    Re: x-x=0?

    Your equation is x2=1. x=1 and x=-1 are the two possible real numbers that satisfy this equation. This means that there are two possible cases, one or the other is true.

    Case 1: x=1; does this satisfy the equation? Yes, 12=1. Then x-x=1-1=0.

    Case 2: x=-1; does this satisfy the equation? Yes, (-1)2=1. Then x-x=(-1)-(-1)=0.

    The two cases do not overlap, one is true or the other one is true, if you consider the original equation with x being 1 sometimes and -1 at other times, perhaps (x)(x)=(1)(-1)=-1 and this doesn't satisfy the equation.

    Of course an equation can give two answers, an equation can give as many answers as there are numbers.
     
  14. Oct 23, 2009 #13
    Re: x-x=0?

    hmm im still not convinced
     
  15. Oct 23, 2009 #14
    Re: x-x=0?

    Then you need to meditate on it, because I don't think any more explanation will help.
     
  16. Oct 23, 2009 #15
    Re: x-x=0?

    when you say

    Of course an equation can give two answers, an equation can give as many answers as there are numbers.

    what do you mean? 1+1 = 2 and only 2?
    2+2=2 and only 2

    the square root of one equals 1 and -1
     
  17. Oct 23, 2009 #16
    Re: x-x=0?

    X = the square root of 1 theres your overlap
     
  18. Oct 23, 2009 #17
    Re: x-x=0?

    I mean exactly what I say. Your equation is a perfect example. x2=1, x=1 satisfies it and x=-1 satisfies it, there are two answers. A cubic equation might have a third solution, a quartic equation might have 4 etc. Consider sinx=0, there are an infinite number of values of x that satisfy it, any multiple of Pi.
     
  19. Oct 23, 2009 #18
    Re: x-x=0?

    if theres an infinite number of values then doesnt that basically mean its meaningless? actually dont explain that i learn too slow... look im sorry i just dont understand why there is no overlap but its fine i can live with it... cheers tho anyway
     
  20. Oct 23, 2009 #19
    Re: x-x=0?

    It is not meaningless, its meaning is that x=nPi where n is any integer.
     
  21. Oct 23, 2009 #20
    Re: x-x=0?

    haha i get it... ok thanks very much... sorry for being a bit dense ha cheers
     
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