Scene: Advanced Calculus II class. I am finishing the proof of the construction Hardy’s zig-zagging continuous everywhere, differentiable nowhere function:
Me: …and so we’ve shown , which proves the function is not differentiable at .
Student A: Can you remind me why?
Me: Sure. Essentially, this argument shows that the difference quotient limit — the derivative — is blowing up at every point simultaneously.
Student B: Huh. You’re like the Michael Bay of calculus.
Me: Get the hell out of my classroom.