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Cell potential is not a state function. Cathode and anode has to do with a single cell at a particular point in time so combining their values gives the cell potential by definition. However, you can't simply find a new cell potential by subtracting some initial value from a final value, so it is not a state function.
Consider E° is an intensive property, meaning that the voltage difference will remain the same and not depend on how many times the reaction occurs. It gives the voltage difference between 2 standard electrodes (cathode-anode) which is always the same.
E is not a state function and because of this we can't apply the same rules as we did for enthalpy and gibbs free energy. It is an intensive property so the value would stay the same no matter how many times the reaction occurs.
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