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ZEROBRAINCAPACITANCE

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HOWEVER, for parallel plate (capacitors) the potential gradient is defined as E = V/d (V being the potential difference). How come there's no negative sign for the potential gradient of the parallel plates?

My book derives it as follows: E = -V/r, but V=V2-V1 (V2 being the lower potential), so E=-(V2-V1)/r and -(V2-V1) = V1-V2, which is the potential difference and r = d, so E = V/d.

HOW? How did they even equate V = V2-V1, when V is just electric potential, fixed for a specific point in space.