There are quite a few questions which involves "showing" $1=2$ or $0 = 1$ or $-1 = 1$ via incorrect algebraic manipulations of $i = \sqrt{-1}$.
Does anyone know if there is a "canonical" question/answer (and if not, would one of our great educators write an answer) that is easily generalisable to at least the usual arithmetic operations?
I'm wondering because of the question " Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$? ". The suggested "duplicate" target is " Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$? ", but I think that for someone who is having difficulties seeing why his/her algebraic manipulations are wrong, the connection between the two questions may not be immediately apparent. (In other words, the answer to the second question may not help.)
And ideally a question of this type should be added to our list here: http://meta.math.stackexchange.com/questions/1868/list-of-generalizations-of-common-questions