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Thread: Proof that -1=1!

  1. #1 Proof that -1=1! 
    Forum Junior Vroomfondel's Avatar
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    I have found an interesting "proof" that i would like to see someone here disprove. It runs as follows:

    1=√1

    1=-1*-1 then

    1=√-1*-1

    since √A*B=√A*√B

    1=√-1*√-1

    since √-1=i

    1=i*i=i^2 so

    1=i^2=-1 thus

    1=-1

    Q.E.D. 8)

    I am not really sure how that can be disputed, lol.


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  3. #2  
    Forum Isotope Zelos's Avatar
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    uve made one fatal error
    1=√(-1x-1)
    1=√(-1x)√(-1 )
    1=i√(x)i=√(x)i^2=-1*√(x)
    then we square the whole shit
    1=(-1)^2*(√(x))^2=x
    all u have proven here is that x=+-1 nothing else. and one of those answers are wrong

    so next time u try to prove something that goes against something so freasking obvius think it throu about a million times before posting it anywhere


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  4. #3  
    Forum Junior Vroomfondel's Avatar
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    hmmmmm....
    I demand that my name may or may not be vroomfondel!
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  5. #4  
    Forum Junior Vroomfondel's Avatar
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    You messed up your math. Ill show you yours and the corrected.

    1=√(-1x-1)
    1=√(-1x)√(-1 )
    1=i√(x)i=√(x)i^2=-1*√(x)
    1=(-1)^2*(√(x))^2=x

    1=√(-1x-1)
    1=√(-1)x√(-1 )
    1=ixi=i^2=-1
    1=(-1)^2

    you tried to bring an x into there out of nowhere. Sorry, you cant do that unless you set x=1!
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  6. #5  
    Forum Professor river_rat's Avatar
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    The problem lies in that the √(-1) as used here is not a well defined continuous function everywhere - it has two branches and thus the step
    √(uv) = √u x √v cannot work in general for non-negative real numbers.

    We have instead that √(uv) = (+-) √u x √v where you have to pick the right sign.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  7. #6  
    Forum Junior Vroomfondel's Avatar
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    That is what i felt was the problem with the "proof." Doesnt really surprise me with the same thing, considering all of the other steps were relatively legitamate.
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  8. #7  
    Forum Isotope Zelos's Avatar
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    i didnt bring x from nowhere, it says 1=-1x-1
    i see a x there, and i uses a x
    if u mean times u should use * not x, it might get confused else
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  9. #8  
    Forum Junior Vroomfondel's Avatar
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    sorry about that. I changed it.
    I demand that my name may or may not be vroomfondel!
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  10. #9  
    Forum Isotope Zelos's Avatar
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    good, cause if i use x as times i could write xxx wich either means x^3 or x times x wich is x^2
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  11. #10  
    Forum Professor river_rat's Avatar
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    Is there no way for the powers that be on this forum to include a latex translator - its a lot easier to just write in latex code and then for it to be rendered into mathematical notation!
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  12. #11  
    Forum Isotope Zelos's Avatar
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    couldnt the leader of this forum add like in MS Words equation program? that would make equations alot easier, both mathematical/physical/chemical
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  13. #12  
    Forum Junior Vroomfondel's Avatar
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    I think I'm gonna go and find a program that makes lines of mathematics to post on forums like this.
    I demand that my name may or may not be vroomfondel!
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  14. #13  
    Forum Professor river_rat's Avatar
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    Vroomfondel - if you are interested in real mathematics and physics then go and learn latex. It is the langauge used in the real academic world and is quite handy to know!

    Anything but ms equation editor Zelos!
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  15. #14  
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    check your 4th line. that equation is true if and only if a and b are non-negative.
    God does not play dice...demi-gods do.
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  16. #15  
    Forum Professor wallaby's Avatar
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    Quote Originally Posted by river_rat
    Is there no way for the powers that be on this forum to include a latex translator - its a lot easier to just write in latex code and then for it to be rendered into mathematical notation!
    i have no idea what a latex translator is but for powers you can use the < sup> < /sup> tags
    note: i have a space in between the first bracket so that the tags will be displayed, you don't want that space.

    E=MC<sup>2</sup>

    Log<sub>2</sub>2<sup>3</sup>

    god dammed logarithms.
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  17. #16  
    Forum Isotope Zelos's Avatar
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    river_rat i dont care if its MS or anything, we need somekinda equation editor ehre
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  18. #17  
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    how u assume 1=root(1)=1;
    aactually it is eq to +_1 na
    I am reddaiah.
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  19. #18 Re: Proof that -1=1! 
    Forum Freshman .:Elusive.Neutrino:.'s Avatar
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    Quote Originally Posted by Vroomfondel
    I have found an interesting "proof" that i would like to see someone here disprove. It runs as follows:

    1=√1

    1=-1*-1 then

    1=√-1*-1

    since √A*B=√A*√B

    1=√-1*√-1

    since √-1=i

    1=i*i=i^2 so

    1=i^2=-1 thus

    1=-1

    Q.E.D. 8)

    I am not really sure how that can be disputed, lol.
    Two things have been forgotten here. First, review your algebra theorems (line 4-- only works with positive integers I believe). Second, root 1 is +/- 1, and you must remember the issue of extraneous solutions.
    <i8b4uUnderground> d-_-b
    <BonyNoMore> how u make that inverted b?
    <BonyNoMore> wait
    <BonyNoMore> never mind
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  20. #19  
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    I think elusive neutrino is right - √(AB) = √A*√B is only valid for positive numbers
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  21. #20  
    Forum Sophomore NimaRahnemoon's Avatar
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    i squared can be 1 or -1, but since -1 makes more sense graphically we accept it as being -1
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  22. #21  
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by Neutrino
    I think elusive neutrino is right - √(AB) = √A*√B is only valid for positive numbers
    √(AB) = √A*√B is true for all real numbers, the problem is that this does not hold for complex numbers because the square root cannot be continuously extended around origin.

    Quote Originally Posted by Nima Rahnemoon
    i squared can be 1 or -1, but since -1 makes more sense graphically we accept it as being -1
    Sorry thats wrong, i^2 = -1 and nothing else. The map x -> x^2 is well defined so you can only have one answer. The ambiquity comes from its inverse, √(-1) = +/- i
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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