Get ready Part 22

For a positive real number $\alpha$ , define $S(\alpha)=\{\lfloor n\alpha \rfloor : n = 1,2,3,\dots\}$ .Is $\{1,2,3,\dots\}$ can be expressed as the disjoint union of three sets $S(\alpha),S(\beta)$ and $S(\gamma)$ ?

Note

• $\lfloor x \rfloor$ denotes the floor function