Can inductor voltage and capacitor current change abruptly?

I understand that inductor current and capacitor voltage cannot change abruptly, but can inductor voltage and capacitor current change abruptly?

I have a feeling the answer is no but I cannot explain why.

Answer

In an ideal world, where a capacitor has no series inductance and an inductor has no parallel capacitance, and voltage and current sources can provide voltages and currents with a step-shaped profile, the current into a capacitor and the voltage over an inductor can change abruptly.

Not that this ideal world is an mathematical abstraction, you can't buy such components.