Algebraic Proof that 1=2
I was writing a post at http://www.dbtechie.com/sql-server/how-to-return-an-empty-set-with-named-columns/ where I made the statement that “1=2” will never be true. This reminded me of my teaching days when I used to baffle my algebra students by proving the absurd, so I decided to post this for all you parents with children of algebra-age. Get them to agree that if you can prove that 1=2, they have to clean the house.
1. Let’s start with a simple mathematical expression that we can all agree upon:
2. Which can also be represented as (distributive property):
3. Or, another way to represent the same thing (think of the pattern for the difference of two squares or multiply it out and you will find it to be true):
4. So taking the equivalent values in step 2 and step 3 we get:
5. Now divide each side by:
yields:
or:
6. Simplify:
7. Divide each side by :
yields:
8. Simplify to yield the desired result:
1 = 2
The reason for this is because we are dividing by zero. It is not as obvious because zero is cloaked as:
Have fun, and if your kids are smart enough to catch you on this one then at least you’ll be cleaning the house by yourself with a smile on your face.
