MathDB

The image that maps

x

1 - x

is called complement, the image that maps

x

\frac{1}{x}

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.

Problem Statement