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Proposition for recognition

Notes:

This proposition leads to a sufficient condition to be a digital line. It helps us recognize a properly digitized straight line from a sequence of pixels.
ki is the length of the short object at digitization level i. The proposition says that all the sequences of natural numbers greater than 1 give a digitization of a straight line according to the necessary condition formulated in the theorem “necessary conditions”.
The proof for rational slopes is based on the euclidic algorithm and the proof for irrational slopes – on the theory for continued fractions.