Odd proof - Can you spot the error?

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February 13th 2010, 11:44 AM
SuperCalculus

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.
February 13th 2010, 11:47 AM
icemanfan

The reason $2(a^2 - ab) = a^2 - ab$ is because $a^2 - ab = 0$ .
February 13th 2010, 11:48 AM
SuperCalculus

Quote:

Originally Posted by icemanfan

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

Indeed, this is correct. Nice one.
February 13th 2010, 11:49 AM
icemanfan

Quote:

Originally Posted by SuperCalculus

Indeed, this is correct. Nice one.

Thanks. For the record, I have never seen that "proof" before.
February 13th 2010, 11:50 AM
pickslides

Quote:

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.

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

Also check your steps, the hole thing seems poorly constructed.
February 13th 2010, 11:54 AM
pickslides

Quote:

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

$a =b$

$a^2 = ab$

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

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

Zero division here

$a+b = b$

$b+b = b$

$2b = b$

$2=1$
February 13th 2010, 12:07 PM
Archie Meade

Quote:

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 ?
February 13th 2010, 12:10 PM
SuperCalculus

Quote:

Originally Posted by Archie Meade

honest ?

Seriously. Shocking, isn't it?
February 21st 2010, 12:17 PM
Aryth

Quote:

Originally Posted by SuperCalculus

Seriously. Shocking, isn't it?

Wow...

Just wow...
February 21st 2010, 03:33 PM
integral

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)
February 27th 2010, 12:16 AM
Bacterius

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.

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.
March 1st 2010, 09:22 PM
harish21

Quote:

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!
March 1st 2010, 09:37 PM
Drexel28

Quote:

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.
March 1st 2010, 09:55 PM
Bacterius

Quote:

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)
March 8th 2010, 03:57 PM
Vertazontal

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.