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Math Help - Math Proof: 2=1

  1. #1
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    Question Math Proof: 2=1

    I dont know if this fourm as seen this before, but its pretty neat, i can prove that 2=1 right?

    Given: a=b


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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Lammalord View Post
    I dont know if this fourm as seen this before, but its pretty neat, i can prove that 2=1 right?

    Given: a=b


    a=b
    a2 =ab
    a2 -b2 =ab-b2
    (a+b)(a-b)=b(a-b)
    Make note: a-b=0

    And math says you can't divide by zero.
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  3. #3
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    ahh wait, let me re-do this, messed something up (its soppost to be squared)

    there, think i fixed that up...


    humm wow, didnt see that one, ahh not even my math teacher last year saw that one...
    Last edited by Lammalord; October 12th 2006 at 01:45 PM.
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  4. #4
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    Quote Originally Posted by Lammalord View Post
    ahh wait, let me re-do this, messed something up (its soppost to be squared)

    there, think i fixed that up...


    humm wow, didnt see that one, ahh not even my math teacher last year saw that one...
    well, I really can't claim credit, I would've missed it too if (I think it was) Glaysher didn't respond to PH's post of this question (although PH knew the answer as well)...

    This is my 800th post!!!!
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  5. #5
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    completion - just for fun

    Quote Originally Posted by Lammalord View Post
    I dont know if this fourm as seen this before, but its pretty neat, i can prove that 2=1 right?...
    Hi,

    I can prove that every number is equal to every number: See attachement.

    EB
    Attached Thumbnails Attached Thumbnails Math Proof: 2=1-agleichb.gif  
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  6. #6
    Member Glaysher's Avatar
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    Quote Originally Posted by earboth View Post
    Hi,

    I can prove that every number is equal to every number: See attachement.

    EB
    Again dividing both sides by c - a - b is dividing by zero and therefore proof invalid.

    If proof was valid you would have derived a contradiction as you had originally assumed a does not equal b. It would not prove all numbers are equal. It would prove that you can only add equal numbers.
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  7. #7
    Senior Member TriKri's Avatar
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    Hi.

    I can prove that 1 = -1. Se below.

    1 = \sqrt{1} = \sqrt{-1 \cdot -1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = -1

    -Kristofer
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  8. #8
    TD!
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    Quote Originally Posted by TriKri View Post
    \sqrt{-1 \cdot -1} = \sqrt{-1} \cdot \sqrt{-1}
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  9. #9
    Senior Member OReilly's Avatar
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    Quote Originally Posted by TriKri View Post
    Hi.

    I can prove that 1 = -1. Se below.

    1 = \sqrt{1} = \sqrt{-1 \cdot -1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = -1

    -Kristofer
    This is proof that Euler shown when the theory of complex numbers was still in it's early stages of development.
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  10. #10
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    Quote Originally Posted by TriKri View Post
    Hi.

    I can prove that 1 = -1. Se below.

    1 = \sqrt{1} = \sqrt{-1 \cdot -1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = -1

    -Kristofer
    It hasn't been proven that \sqrt{-1\cdot-1}=\sqrt{-1}\cdot\sqrt{-1}
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  11. #11
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    It hasn't been proven that \sqrt{-1\cdot-1}=\sqrt{-1}\cdot\sqrt{-1}
    I would HOPE that it hasn't been proven!

    -Dan
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  12. #12
    Senior Member TriKri's Avatar
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    Quote Originally Posted by Quick View Post
    It hasn't been proven that \sqrt{-1\cdot-1}=\sqrt{-1}\cdot\sqrt{-1}
    I suppose not, I mean, I really hope it hasn't!
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  13. #13
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    Proof that it isn't:

    √(-1 * -1) ≠ √(-1) ^ 2
    √(1) ≠ i ^ 2
    1 ≠ -1

    Heh. That was probably obvious, but I love doing short proofs like that.

    ...Well, I guess I just said the opposite of what the origonal problem said. It makes my brain hurt.
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  14. #14
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    Quote Originally Posted by The Pondermatic View Post
    Proof that it isn't:

    √(-1 * -1) ≠ √(-1) ^ 2
    √(1) ≠ i ^ 2
    1 ≠ -1

    Heh. That was probably obvious, but I love doing short proofs like that.

    ...Well, I guess I just said the opposite of what the origonal problem said. It makes my brain hurt.
    There are like 3 errors in that proof!

    First the preservation of the not equality was not used properly
    Second the use of illegal math factorizations
    Third a mathematical logical error.

    But yet what you said in conclusion was completely true!
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  15. #15
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    Really?

    *looks back at his work, fails to see problems*

    Heh, I guess i'm a bit of a newb.

    What exactly did I do wrongly again?

    I have to admitt, though, if my proof really is wrong, that's pretty cool that it's right anyway.
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