let a = b

Discussion in 'Off Topic' started by callumacrae, Oct 22, 2010.

  1. callumacrae

    callumacrae not alex mac Community Support

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    let a = b
    -> a^2 = b^2 = ab
    -> a^2 - b^2 = a^2 - ab
    -> (a+b)(a-b) = a(a-b)
    divide by (a-b)...
    -> a+b = a
    as b=a..
    -> a+a = a
    -> 2a = a
    divide by a..
    -> 2 = 1
    -> 1 = 0 (-1)
    -> a = 0 (*a)

    This proves that 1=2, 0=1, and in general, any number is equal to 0.

    ...im confused

    ~Callum
     
  2. Gouri

    Gouri Community Paragon Community Support

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    In mathematics you can't divide anything by zero

    In the above

    you said

    That can't be done as a=b you can't divide by (a-b) as it is dividing by zero.

    that is mistake in the whole process.

    :)
     
  3. ChatIndia

    ChatIndia Community Advocate Community Support

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    This is the puzzle in the first few pages on "mathematical games and puzzles" by Rajesh kumar Thakur. I've already seen this absurd problem.
     
  4. callumacrae

    callumacrae not alex mac Community Support

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    You can, anything divided by 0 is Infinity :)

    ~Callum
     
  5. Gouri

    Gouri Community Paragon Community Support

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    then in that step the equation becomes

    infinity = infinity

    then where the remaining steps comes from.....

    :)
     
    Last edited: Oct 22, 2010
  6. callumacrae

    callumacrae not alex mac Community Support

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    Yey all fixed :D

    I am no longer confused :)

    ~Callum
     
  7. ChatIndia

    ChatIndia Community Advocate Community Support

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    If you wish I'll prove this using complex number concept as well. lol
     
  8. descalzo

    descalzo Grim Squeaker Community Support

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    So,

    [​IMG] / 0 =

    [​IMG]
     
  9. ChatIndia

    ChatIndia Community Advocate Community Support

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    -1/1 = 1/-1

    taking square root on both sides

    (-1/1)^1/2 = (1/-1)^1/2

    now as i^2 = -1

    i/1 = 1/i

    now dividing by 2 on both sides

    i/2 = 1/2i

    adding 3/2i on both sides

    and now multiplying by i on both sides

    i^2/2 +3/2 = 1/2 + 3/2

    -1/2 + 3/2 = 4/2

    1= 2

    ---------- Post added at 07:07 PM ---------- Previous post was at 07:06 PM ----------

    gsonline going to find fault in this. :)

    ---------- Post added at 07:16 PM ---------- Previous post was at 07:07 PM ----------

    I would like to correct gsonline. "in mathematics we cannot divide by zero". Its infinity as said by alex. Actually we don't have discovered what 0/0 is yet. (a+b)(a-b)/(a-b)

    = (a+b)0/0

    = 0/0

    did you get the mistake.
     
  10. callumacrae

    callumacrae not alex mac Community Support

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    By (-1/1)^1/2 I'm assuming you mean (-1/1)^(1/2)?

    I like complex numbers :)

    ~Callum
     
  11. ChatIndia

    ChatIndia Community Advocate Community Support

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