A "letter T" erected at point A of the x-axis in the xy-plane is the union of a segment AB in the upper half-plane perpendicular to the x-axis and a segment CD containing B in its interior and parallel to the x-axis. Show that it is impossible to erect a letter T at every point of the x-axis so that the union of those erected at rational points is disjoint from the union of those erected at irrational points.
A.Csaszar geometryrectanglereal analysisreal analysis unsolved