### The Harding Theorem

a=b
a^2=ab
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
(a+b)(a-b)/(a-b)=b(a-b)/(a-b)
a+b=b

Therefore, if a=1, then 1=2

When I was in 9th grade, my chemistry teacher, Dr. Fred Harding, wrote this onto the board. I loved it so very much I copied it down and put it into my wallet. For the longest time no one could tell me why it was wrong. I love to pull it out when people told me how smart they were and watch them squirm, or as I did, joyously exclaim that math was broken. Obviously math isn't broken, but it took me many more years to learn what was actually going on.

The handwritten formula was transferred between one paper to the next several times through the years. When one would wear out, I would create another. Kept behind my driver's license for another 12 years it met its match when I showed it to my math professor in college. She didn't immedately know what was wrong about it, but her gut feeling told her it was wrong. A few days later she came back and told me the thing that again restored my faith in math. You cannot divide by zero.

If you were to substitute A with a given number and attempt to work the formula, it breaks down in an obvious way.

I still enjoy this reminder of my youth, and provide it here (taking no credit) for the curiosity that it is.

Naw, just Pre-Calc and Environmental Geology. The formula is from my days of high school.
Fred Harding, my chemistry teacher showed us that.
It's wrong, but it looks nice.
Anonymous said…

http://www.icengineering.com/n3ic/wrongs.gif
I've always been a fan of that Farside comic. :-)
Anonymous said…
Heh - for me that could be said of about 90% of all Far Side comics. :)
Hmm... Substitution...
2=2

2^2=2*2
4=4

2^2-2^2=2*2-2^2
4-4=4-4

(2+2)(2-2)=2(2-2)
(0)(0)=2(0)
0=0

(2+2)(2-2)/(2-2)=2(2-2)/(2-2)
(0)(0)/(0)=2(0)/(0)
Cannot divide by zero

2+2=2
Incorrect