Sorry this may sound like a silly question and I know that this does't meet the quality standards of Math S.E, I found this in one of the Math-Jokes websites and found it interesting,
$$x=1$$ $$\frac{d}{dx} x=\frac{d}{dx} 1$$ $$1=0$$
What I think is the problem is that it is not differentiable, saying $x=1$ is equivalent to saying $y=\delta(x-1)$, which as we know is not continuous at $x=1$, and so it is not differentiable. is this right? or is there some other reason to resolve the paradox?