a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x] You may doubt that 2=1. So, where is the mistake? Think about it.
You may not like the first step (a=x). But, we do this kind of thing all the time in Algebra. It's true for plenty of a's and x's. Assume that a is the number of ears on my head, and x is the number of ears on your head. In that case a=x (if a is not equal to x, forgive me for mentioning it).
Anyway, all of the steps are perfectly legal, dividing both sides by a-x is the last one. What is a-x? Well, a=x (step 1), so a-x=0. In the last step, we divided by zero.
OH MY GOD! I divided by 0!!!!!!
Home
Register
Login
