What is the proof of complete ionic dissociation in water?
One method is by making electrical conductivity measurements on aqueous solutions of salts. If we take four strong electrolytes:


Sodium chloride
Potassium chloride
Sodium perchlorate
Potassium perchlorate


We can measure the electrical conductivities at very low concentrations which allows us to obtain the limiting specific conductivties of the salts (extrapolation to zero concentration).

We will then find that the sum of the limiting conductivity of sodium chloride and potassium perchlorate will be the same as that of potassium chloride and sodium perchlorate.

This is because the limiting conductivity of a strong electrolyte salt is the sum of the contributions of the cations and anions. This allows us in an indirect way to show that some salts can totally dissociate when very dilute.