 If (x0, y0) and (x1, y1) are two points of the plane ℝ2, define (x0, y0) < (x1, y1)

if y0 = y1 and x0 < x1.This is a partial ordering of ℝ2 under which two points are comparable only if they lie on the same horizontal line.The maximal totally ordered sets are horizontal lines in ℝ2.