DLC Blog

2 = 1 !?

Let’s take a look at this proof.

1. Let “A” and “B” equal non-zero number
A = B
2. Multiply both sides by A
A^2 = AB
3. Subtract B^2
A^2 – B^2 = AB – B^2
4. Factor both sides
(A+B)(A-B) = B(A-B)
5. Divide both sides by (A-B)
A+B = B
6. Since A = B, plug B for A
B+B = B
7. Combine the like terms
2B = B
8. Divide both sides by B
2 = 1

Hmm… is this possible?? Can you see what’s wrong with this?
These mathematical proofs are called invalid proofs and the proofs look right, but there is an obvious contradiction. The proofs are flawed, of course, but then the flaw is well hidden or subtle.

Well, if you plug real numbers into A and B from the beginning, you can easily see why this is wrong. The flaw is in step 5. Let’s take a look:

1. Let “1” and “1” equal non-zero number
1 = 1
2. Multiply both sides by 1
1^2 = 1*1
3. Subtract 1^2
1^2 – 1^2 = 1*1 – 1^2
4. Factor both sides
(1+1)(1-1) = 1(1-1)
5. Divide both sides by (1-1)
1+1 = 1

Wait, (1-1) = 0. You CANNOT divide by the 0 because division by 0 is undefined.

Hope you enjoyed a little mathematical trick.
For more information, please here here and then click “proof”.

Miyagi

Posted by Hayato on December 3, 2006 04:07 PM.