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**a*^{2}=*a**b*

- Subtract
*b*^{2}*a*^{2}−*b*^{2}=*a**b*−*b*^{2}

- Factor both sides
- (
*a*−*b*)(*a*+*b*) =*b*(*a*−*b*)

- (
- Divide out (
*a*−*b*)*a*+*b*=*b*

- Observing that
*a*=*b**b*+*b*=*b*

- Combine like terms on the left
- 2
*b*=*b*

- 2
- Divide by the non-zero
*b*- 2 = 1

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

## Vasko

March 16, 2007 6:55 amYou cannot “Divide out (a − b)” because a=b and a-b=0. You cannot divide by 0 🙂 .

## Adam

March 16, 2007 8:08 amNice, that’s correct! Or should I say; that’s what makes my proof incorrect ; )

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## shadowman

March 16, 2007 4:06 amHi! How r u?

nice site!

## Adam

March 16, 2007 4:16 amI am doing well, thank you for the positive comment 🙂

Take Care!

## salman

March 16, 2007 8:41 amnice work a person can learn more n more

## daisy

March 16, 2007 11:49 pmtrue or false: a^2-b^2=(a-b)^2

## ashley

March 16, 2007 12:42 amwhy did you subtract b squared? where did that come from???

## Saud

March 16, 2007 8:27 amWell,

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.

## admin

March 16, 2007 2:31 amThis 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 🙂