The image that maps x to 1−x is called complement, the image that maps x to x1 is called invert. Two numbers x and y are called related if they can be transferred into each other by means of complementation and/or inversion. A family is a collection of numbers where every two elements are related. Determine the maximum size n of such a family.
Show that the number line can be divided into n parts, such that each of those n parts contains exactly one number from each n-number family. combinatoricsalgebrafunction