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.....Plus, the aperture size number is based on DISTANCE from the FP to the Focal AREA. (The film or sensor). so the numbers are the same because the MOUNTING distance is the same on a FF v Crop.........
And this can readily be observed by taking two lenses of different focal lengths and setting them to the same aperture. Set them side-by-side so you can see through both, and the opening created by the aperture blades will be different sizes.