In Our World, 2=1

Let us take two variables a and b

Let a=b

Therefore, a2=ab

Therefore, a2-b2=ab-b2 (Subtracting b2 from both sides)
Therefore, (a+b)(a-b)=b(a-b) (using identiy a2-b2 = (a+b)(a-b)

Therefore, a+b=b (Dividing (a-b) from both sides)

Since a=b, we can substitute a in place of b

Therefore, a+a=a

Therefore, 2a=a

Therefore, 2=1

In out world, two is equal to one.

Hence, proved.



  1. Mridul Kapoor · September 3, 2009

    See, this is absolutely wrong
    you assumed let a=b
    so this implies a-b=0

    When you are dividing by a-b on both sides: you are dividing by zero on both sides.
    Which is in fact not allowed. Division by zero is not allowed!!

    • Aditya · September 3, 2009

      Well, in fact, you caught it. In class, we found out the mistake. The fun is, that everybody believes it at first sight. Everyone is stumped.

  2. karmanya · September 3, 2009

    Are you in AVTE? I remember Vipin sir talking about this in class once. Question is, can you figure out the error? 🙂 Its pretty simple, read it again

  3. Rish · September 4, 2009

    Haha. nice. 🙂 ur blogs are fun dude!

  4. Shikhar · September 6, 2009

    Nice trick. But division with zero is not defined. If dividing or multiplying with zero was accepted, you would need not study how to prove anything in mathematics!!
    To prove: LHS =RHS
    Proof: LHS×0=0 and also RHS×0=0
    Hence, proved that LHS=RHS!

  5. boo boo bear · September 15, 2009

    Thanks for ur help… My algebra II teacher is always making us do this hard stuff in class. Ur blog really helped! =)

    • Aditya · September 15, 2009

      Heh. But this stuff is pretty ridiculous. Don’t take it as serious math.

  6. arjun · September 16, 2009

    another one of those, more trickier than dividing by zero:
    x^2 = x + x + x … x times

    differentiating both sides wrt x
    2x = 1 + 1 + 1 … x times
    => 2x = x
    => 2 = 1 or x = 0 (which is not true)
    => 2 = 1

    • Aditya · September 16, 2009

      Er, first of all, thank you for commenting! Second, I’ve have no clue what differentiation means.
      Thirdly, won’t x2=x*x*x* rather than x+x+x?

  7. arjun · September 19, 2009

    x^2 = x * x
    a * b = a + a + a +… b times
    => x * x = x + x + x…x times
    you’ll get to know derivatives in class 11th, and the soln of this prob in 12th. try it then

  8. Mrittunjoy Guha Majumdar · September 30, 2009

    Its Not MGM I Hope You Get Who I Am.
    Here’s Another Trick.
    Let x=y
    So 2x-x=2y-y
    So 2x-2y=x-y
    So 2(x-y)=x-y
    Say Goodbye To x-y
    Hence 2=1
    But As Shekhar Stated x-y=0
    And Division With 0 Is Not Defined
    Hence These Are All Useless

  9. Mrittunjoy · October 17, 2009

    Good discussion. That was a pretty differential calculus demonstration for some interested bunch of Montfortians. The real fun is in partial differentiation and implicit functions. Who is this impersonator, by the way?

    • Mrittunjoy · October 17, 2009

      It was to be a “pretty ‘lame’ diff…”. Some errors there.

    • Aditya · October 18, 2009

      That imposter is my classmate. Gee. I don’t even know what calculus is, so I can’t comment.

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