1. ## 1 = 2

Found this highly amusing mathematical proof that concluded that 1 = 2, so without further ado, here it is.

1. Let A = B

2. Multiply both sides by A.

A^2 = AB

3. Add (A^2 - 2AB) to both sides

A^2 + A^2 - 2AB = AB + A^2 - 2AB

4. Factor the left side of the equation, and collect right terms on the right

2(A^2 - AB) = A^2 - AB

5. Divide both sides by (A^2 - AB)

2 = 1

2. i've seen it before.
xisnotx, get it?
it's the exact same proof.
you can define x as anything, even what it can't possibly be.
therefore, logic is limiting.

3. Originally Posted by Alea_iacta_est
1. Let A = B

5. Divide both sides by (A^2 - AB)
This pains my soul.

4. There are several variations on a theme of this proof. The error with all of them is division by zero (because A = B, the expression you factor out is zero, and 0*X = 0*Y is true for all values X and Y).

5. Originally Posted by nemo
This pains my soul.
Mine too.

I like this one a bit better:
1=sqrt(1)=sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i*i=-1.

6. Originally Posted by ygolo
Mine too.

I like this one a bit better:
1=sqrt(1)=sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i*i=-1.
That is indeed a conundrum.

7. Originally Posted by Alea_iacta_est
Found this highly amusing mathematical proof that concluded that 1 = 2, so without further ado, here it is.

1. Let A = B

2. Multiply both sides by A.

A^2 = AB

3. Add (A^2 - 2AB) to both sides

A^2 + A^2 - 2AB = AB + A^2 - 2AB

4. Factor the left side of the equation, and collect right terms on the right

2(A^2 - AB) = A^2 - AB

5. Divide both sides by (A^2 - AB)

2 = 1
Wrong because A = B and you forgot that halfway.

Explanation:

Originally Posted by Alea_iacta_est

1. Let A = B

2. Multiply both sides by A.

AA = AB

3. Add (AA - 2AB) to both sides

AA + AA - 2AB = AB + AA - 2AB

4. Factor the left side of the equation, and collect right terms on the right

Consider A=B

X = A or B

XX + XX - 2XX = XX + XX - 2XX
X = X
Just because of a misuse of the to the power symbol, does not mean something that is logic, suddenly isn't.

8. Originally Posted by ygolo
Mine too.

I like this one a bit better:
1=sqrt(1)=sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i*i=-1.
Just "-1 * -1 = 1" is enough to see the logical conundrum, but then, so is -1 or any negative number in fact. It is impossible to have -1 of something after all.

9. Originally Posted by Alea_iacta_est
5. Divide both sides by (A^2 - AB)

2 = 1
If A=B, then A^2 = AA = AB, and anything minus itself is zero. You can't divide by zero.

null = null... noting new about that.

10. Originally Posted by ygolo
Mine too.

I like this one a bit better:
1=sqrt(1)=sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i*i=-1.
Are you sure that 1=sqrt(1)?

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