# Does 2 equal 1?

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

#### 9 Comments

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

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

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I am doing well, thank you for the positive comment 🙂

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nice work a person can learn more n more

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

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

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.

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 🙂