The Derivative Dilemma
We all have seen the logic-defying calculations proving $1=2$ in school, haven’t we? The simple ones are based on the mathematical fallacy of division by zero i.e., cancelling an algebraic expression from both sides which is equal to zero. I have one such trick calculation to show you, it is a bit more sophisticated (than division by zero) based on the concept of “derivative”. The problem goes as follows, $x^2$ can be written as a sum like this: \begin{align} x^2=x+x+x+\cdots +x \qquad \textit{ x times} \end{align}...