It is not hard to see that the set of 3 points with coordinates (1, 0), (0, 1), and (-1, 0) can shattered by axis-aligned squares: e.g., to label positively two of these points, use a square defined by the axes and with those to points as corners. Thus, the VC-dimension is at least 3. No set of 4 points can be fully shattered. To see this, let Pr be the highest point, PB the lowest, Pr the leftmost, and PR the rightmost, assuming for now that these can be defined in a unique way (no tie), the cases where there are ties can be treated in a simpler fashion. Assume, without loss of generality, that the difference der of y-coordinates between PT and PB is greater than the difference dar of x-coordinates between Pr and PR. Then, PT and PB cannot be labeled positively while Pr and PR are labeled negatively. Thus, the VC-dimension of axis-aligned squares in the plane is 3