Wait, wait, wait … 1=2?

Assumption #2: Whatever modification you make upon the left side of the equal sign must also be done upon the second side. In other words, since x=y, anything I may add unto x I must also add unto y, and any other operation that I perform upon x must also be performed upon y.

Argument :: Thus, since x = y:

Step 1.) Multiply both sides by x: x*x = x*y

Step 2.) Subtract y*y from both sides: x*x – y*y = x*y – y*y

Step 3.) Factor both sides: (x+y)(x-y) = y(x-y)

Step 4.) Divide out the common factor, (x-y), on both sides:

Step 5.) So now we have (x+y) = y … but wait! What was our original statement? If x = y then we can substitute x in for each y giving us:

(x+x) = x

2x = x

Step 6.) Divide both sides by x:

Whoa! We are left with 2 = 1

But wait, there’s more! If 2 = 1 then I can multiply both sides by 2 and get 4 = 2 … but if 1 = 2 and 2 = 4, then 1 also equals 4!!! In fact, I can effectively claim that every number equals every other number!

Next time you are at the store, by demonstrating your superior mathematical ability, you should be able to pay $1 for absolutely anything since 1 equals any amount they could be asking for (don’t feel offended if this doesn’t actually happen).

Or…you can check out this video on The Four Rules of Algebra that explains where we might have gone wrong. (Note: You must be logged in to your free account to watch the video tutorials. Don’t have an account yet? Sign up here.)

*-ish

**To people that don’t know anything about algebra.