Does 2 equal 1?

March 16, 2007  |  Geeky, Math, Uncategorized

Does 1 equal 2, you tell me? 😉 Here is the proof (unfiltered by rational arguments):

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  • Let a and b be equal non-zero quantities
    a = b
  • Multiply through by a
    a2 = ab
  • Subtract b2
    a2b2 = abb2
  • Factor both sides
    (ab)(a + b) = b(ab)
  • Divide out (ab)
    a + b = b
  • Observing that a = b
    b + b = b
  • Combine like terms on the left
    2b = b
  • Divide by the non-zero b
    2 = 1

Well, can you spot the mistake? 🙂 Click here to subscribe to this Blog

About the author

ABDERISAK ADAM is an author, blog writer and a PhD candidate in the institution of Civil and Environmental Engineering at Chalmers University of Technology. He is also the owner and webmaster of www.study-habits.com, a website dedicated to the discussion of study techniques in the context of higher education. Adam is the author of a number of publications including 'The Study Guide PRO'. You can connect with him through Google+, Linkedin or by submitting a form.


9 Comments


  1. You cannot “Divide out (a − b)” because a=b and a-b=0. You cannot divide by 0 🙂 .

  2. Nice, that’s correct! Or should I say; that’s what makes my proof incorrect ; )

  3. Hi! How r u?
    nice site!

  4. I am doing well, thank you for the positive comment 🙂
    Take Care!

  5. nice work a person can learn more n more

  6. true or false: a^2-b^2=(a-b)^2

  7. why did you subtract b squared? where did that come from???

  8. Well,
    a + b = b
    i.e a = b – b
    i.e a = 0
    which contradicts the first statement of the proof that a and b are non zero quantities.
    Thus, the proof is incorrect.

    Another method(which does not make sense, actually):
    We know that,
    0! = 1
    and 1! = 1
    This proves that,
    0! = 1!
    Cancelling factorial sign(!) on both sides, we get,
    0 = 1 😛

    The blog is pretty good:) I loved all the posts.

  9. This part of the “proof” was actually valid. Remember, you can always do ‘what ever’ you want to one side of the equation as long as you do the same on the other. x=2 is the same as x-1=2-1 🙂

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