Here is a little maths teaser for you. Since I was a student, I always loved those “proofs” that zero equals one. Of course, most of the time, this was achieved by sneakily dividing by zero somewhere along the way.
But yesterday I came across a proof that used a different, slightly more subtle trick and uses complex numbers. I apologise to any reader not familiar with complex numbers. Anyone interested can find a quick introduction here.
Enough introduction, here is the “proof”:
Looks OK, but it can’t be right of course. So where is the error in this equation? Can you find out?
You can find the answer here.