Thread: Odd proof - Can you spot the error?

1. Odd 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.

2. The reason $\displaystyle 2(a^2 - ab) = a^2 - ab$ is because $\displaystyle a^2 - ab = 0$.

3. Originally Posted by icemanfan
The reason $\displaystyle 2(a^2 - ab) = a^2 - ab$ is because $\displaystyle a^2 - ab = 0$.
Indeed, this is correct. Nice one.

4. Originally Posted by SuperCalculus
Indeed, this is correct. Nice one.
Thanks. For the record, I have never seen that "proof" before.

5. Originally Posted by SuperCalculus

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

Hence, 2=1?!
You have divided by 0, which is impossible to do.

$\displaystyle a = b \implies a-b=0$

Also check your steps, the hole thing seems poorly constructed.

6. Originally Posted by icemanfan
Thanks. For the record, I have never seen that "proof" before.
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

$\displaystyle a+b = b$

$\displaystyle b+b = b$

$\displaystyle 2b = b$

$\displaystyle 2=1$

7. Originally Posted by SuperCalculus
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.
honest ?

8. Originally Posted by Archie Meade
honest ?
Seriously. Shocking, isn't it?

9. Originally Posted by SuperCalculus
Seriously. Shocking, isn't it?
Wow...

Just wow...

10. 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

11. This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.

high school teachers are mostly idiots who only know what the school expects them to teach.
Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.

12. Originally Posted by Bacterius
This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.

Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.
Haha. This reminds me of my high school teacher who did not know the spelling of Epsilon! And he had a MS in Physics!

13. Originally Posted by Bacterius
This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.

Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.
My High school teach Mr. Pillion is the one that kindled my love for math. He may not have been a theoretician but his love for Calculus was all it took.

14. Originally Posted by Drexel28
My High school teach Mr. Pillion is the one that kindled my love for math. He may not have been a theoretician but his love for Calculus was all it took.
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)

15. 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.