Hard shadows in real life

I was thinking the other day and it occurred to me that a perfect hard shadow is impossible in real life due to the fact that:

lim sqrt(dx^2 + dy^2 + dz^2) != 0
dx->0
dy->0
dz->0

dx, dy, dz being the difference between the shadow caster’s sample point and the potential shadow sample point.

and dx ≠ 0 and dy ≠ 0 and dz ≠ 0 because then the shadow caster and the sample point would be at the same position.

Essentially, the idea is that a perfect hard shadow requires the shadow caster and the sample point to be infinitely close to each other

is this correct or is this some garbage that i thought up that has no meaning lol