In the first section of "Basic Notions of Algebra", Shafarevich used sets under mod 3 arithmetic to introduce the idea of coordinates and thus constructed finite number systems in order to coordinatise finite geometries, however I get lost after $I = (W,W) $, why is $AFH$ is given by $$VX + VY = U$$, and $DCH$ by $$VX + WY = V$$? It does not make sense for me, since the we can verify that $V+W = U$.
