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The number associated with a point is the coordinate of the point. As long as the context is clear, we will follow the standard convention of using the real number for both the name of the point and its coordinate
This presupposes several things. First, that real numbers are parasitic, and that the first class citizens of this ontology are the points. Second, that the number is only ever the index of the point, or some property (coordinate) of the point. Disgusting.