A sloped plane can be "roughened" at an infinitesimal scale to produce a union of horizontal and vertical surfaces, without changing the total surface vector. At each "step", the total surface vector assigned to the step is approximately equal to the total surface vector assigned to the corresponding portion of the flat plane, the error originating from the infinitesimal portions at the step's ends. The total contributions of the infinitesimal errors at the ends of each step to the total surface vector diminishes to 0 as the steps get smaller and smaller.
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