MathDB
mean-free order

Source: miklos schweitzer 1994 q1

October 16, 2021
ordered set

Problem Statement

An ordered set of numbers is mean-free if for all x<y<zx < y < z , yx+z2y \neq \frac{x + z}{2}. Is it possible to order the real numbers so it becomes mean-free?
related: https://www.youtube.com/watch?v=ppaXUxsEjMQ