Let a = b.

Hence, a^2 = ab.

So, 2a^2-2ab = a^2 - ab

2(a^2-ab) = 1(a^2-ab)

Hence, 2=1?!

I showed this to two maths teachers at my school who couldn't figure this... Let's see how you guys fare.

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- Feb 13th 2010, 11:44 AMSuperCalculusOdd proof - Can you spot the error?
Let a = b.

Hence, a^2 = ab.

So, 2a^2-2ab = a^2 - ab

2(a^2-ab) = 1(a^2-ab)

Hence, 2=1?!

I showed this to two maths teachers at my school who couldn't figure this... Let's see how you guys fare. - Feb 13th 2010, 11:47 AMicemanfan
The reason $\displaystyle 2(a^2 - ab) = a^2 - ab$ is because $\displaystyle a^2 - ab = 0$.

- Feb 13th 2010, 11:48 AMSuperCalculus
- Feb 13th 2010, 11:49 AMicemanfan
- Feb 13th 2010, 11:50 AMpickslides
- Feb 13th 2010, 11:54 AMpickslides
I have seen ti many times, it goes like this

$\displaystyle a =b$

$\displaystyle a^2 = ab$

$\displaystyle a^2-b^2 = ab-b^2$

$\displaystyle (a-b)(a+b) = b(a-b)$

Zero division here

$\displaystyle a+b = b$

$\displaystyle b+b = b$

$\displaystyle 2b = b$

$\displaystyle 2=1$ - Feb 13th 2010, 12:07 PMArchie Meade
- Feb 13th 2010, 12:10 PMSuperCalculus
- Feb 21st 2010, 12:17 PMAryth
- Feb 21st 2010, 03:33 PMintegral
It is not surprising. I have come to learn over the years, high school teachers are mostly idiots who only know what the school expects them to teach. Which is not much (Rofl)

- Feb 27th 2010, 12:16 AMBacterius
This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.

Quote:

high school teachers are mostly idiots who only know what the school expects them to teach.

- Mar 1st 2010, 09:22 PMharish21
- Mar 1st 2010, 09:37 PMDrexel28
- Mar 1st 2010, 09:55 PMBacterius
Aww, teaching is so much more, so much more effective when the teacher enjoys what he's talking about, it really gives a different feel to the lesson (as I experienced it in biology). Sadly this world is not about a better education but about higher profit :( (high school teachers are cheap to manufacture)

- Mar 8th 2010, 03:57 PMVertazontal
Ignoring the last equation and simplifying the second to last one, I got 2A^2-2A^2=A^2-A^2, which is of course 0=0.

I know it's late, but I didn't look at all your guys' answers and solved it on my own, and wanted to check if my solution was correct.