Mathematical proof for convergence Sloppy Algorithm, convergence demonstrations, and differences between the Sloppy Algorithm and dithering.

This document has five sections. Section 1 has a proof for the convergence of the Sloppy algorithm. Section 2 shows how the magic number is explicitly computed when and f(L) = L. Section 3 gives the condition when a useful magic number can be found. Section 4 gives an example where a person is part of the Sloppy Algorithm and has the task of determining the absolute gray-scale value. Section 5 describes the differences between sloppy rulers and dithering.
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