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    Huh? It took you 4 weeks to read this thread?
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    (Original post by mockel)
    Huh? It took you 4 weeks to read this thread?
    Hmm

    OK, looks like I just thought I was on the last page but was simply just on the last post of page 2. That makes more sense. I think I'll go away now.
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    Am i a genious or a complete idiot?
    the latter

    Mainly because I don't understand what you're on about :p:
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    Vazzyb's Hypothesis: 2 = 1

    if a = b
    then a^2 = ba (times both sides by a)
    and a^2 + a^2 - 2ab = ba + a^2 - 2ab (adding a^2 - 2ab to each side)
    and so, factorising, 2(a^2 - ab) = 1(a^2 - ab)
    cancel a^2 - ab, from both sides, and you are left with

    2 = 1. Q.E.D.

    Please don't blurt the answer out if you are a. doing further maths and in your second year or b. in university and above...

    Everyone else can try! Winner gets rep!
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    (Original post by Vazzyb)
    Vazzyb's Hypothesis: 2 = 1

    if a = b
    then a^2 = ba (times both sides by a)
    and a^2 + a^2 - 2ab = ba + a^2 - 2ab (adding a^2 - 2ab to each side)
    and so, factorising, 2(a^2 - ab) = 1(a^2 - ab)
    cancel a^2 - ab, from both sides, and you are left with

    2 = 1. Q.E.D.

    Please don't blurt the answer out if you are a. doing further maths and in your second year or b. in university and above...

    Everyone else can try! Winner gets rep!
    My maths teacher used this one on us when I did Further Maths , I won't type the answer though, but in quite a lot of these problems its just a matter of identifying the step where (to a mathematician) the unimaginable and sacrilicous sin happens :p: .
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    Ah hehe, I can do this one ^_^ !

    If you have 2(a² - ab) = a² - ab, and you divide by 'a² - ab', you are effectively dividing by 0, because a² - ab = a² - a² = 0.

    The last step shows 2*0 = 1*0, but you can't then divide by 0 ...
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    (Original post by Vazzyb)
    AHH! That was bad...It is amazing how many geniouses we have on this forum

    But here is a slightly better one,

    ok let

    x^2 + x + 1 = 0

    (times by x) x^3 + x^2 + x = 0
    (add 1 to both sides) x^3 + x^2 + x + 1 = 1
    (but we know that x^2 + x + 1 = 0), therefore, x^3 + 0 = 1
    x^3= 1
    x = 1
    therefore, because of the original definition,
    1 + 1 + 1 = 0
    3 = 0

    wow!
    Whats the solution to that?
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    (Original post by Enfalas)
    Whats the solution to that?
    I think somebody already mentioned this but:

    x³ = 1 has 3 solutions (1 real, 2 complex).
    x² + x + 1 = 0 has 2 solutions (2 complex).

    VazzyB selects the real one for x³ = 1 , which is x = 1 (ignoring both of the complex roots), but this doesn't satisfy the quadratic .
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    have any of you heard of Islam's Theorem? it states 0 = ∞, and every other number does not exist.
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    (Original post by chewwy)
    have any of you heard of Islam's Theorem? it states 0 = ∞, and every other number does not exist.
    That was actually my unproved theory...
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    (Original post by Casey)
    I think somebody already mentioned this but:

    x³ = 1 has 3 solutions (1 real, 2 complex).
    x² + x + 1 = 0 has 2 solutions (2 complex).

    VazzyB selects the real one for x³ = 1 , which is x = 1 (ignoring both of the complex roots), but this doesn't satisfy the quadratic .
    I think I get you... I'm only doing AS maths... That's why I was a bit confused...

    So basically the 2 complex solutions (ie. roots of negative numbers) would fit both equations?
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    (Original post by Enfalas)
    I think I get you... I'm only doing AS maths... That's why I was a bit confused...

    So basically the 2 complex solutions (ie. roots of negative numbers) would fit both equations?
    If x² + x + 1 = 0
    .. (x+½)²-¼+1 = 0
    .. x = -½ ± √(-3/4)

    so x = -½ + √3/2i and x = -½ - √3/2i

    By completing the square. To check these x-values, you can substitute them back into quadratic equation and expand and get 0.
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    (Original post by chewwy)
    have any of you heard of Islam's Theorem? it states 0 = ∞, and every other number does not exist.
    What?
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    (Original post by V.P. Keys)
    If x² + x + 1 = 0
    .. (x+½)²-¼+1 = 0
    .. x = -½ ± √(-3/4)

    so x = -½ + √3/2i and x = -½ - √3/2i

    By completing the square. To check these x-values, you can substitute them back into quadratic equation and expand and get 0.
    I thought you meant something like that..
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    ok, maybe im strange but i just considered the posibility that 1 doesnt = 1...

    for an instant i thought it possible, then the idea (dont even know what or why) flew away...

    have u people ever had this rushes of inspiration where u suddenly feel more inteligent and for instances u see really increadible things??

    (or was it just me an my pills... )
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    (Original post by Candy-Kills)
    ok, maybe im strange but i just considered the posibility that 1 doesnt = 1...
    It would completely contradict the definition of = if a != a.
    (Original post by Candy-Kills)
    have u people ever had this rushes of inspiration where u suddenly feel more inteligent and for instances u see really increadible things??
    I've certainly had moments where suddenly everything snaps into place and becomes easier to understand. Sort of like seeing a magic eye picture.
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    nice to know im not alone in this world...
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    By chance I just had one of those 'Ohhhh.... so that's how it all fits together!' moments about 20 minutes First I thought 'Ah crap, I don't understand what's going on at all' then it flipped to making perfect sense
 
 
 
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