Show that there exists a proper non-empty subset $S$ of the set of real numbers such that, for every real number $x$, the set $\{nx + S : n \in N\}$ is finite, where $nx + S =\{nx + s : s \in S\}$
Source: Danube 2013 p4
Tags: Sets, set theory, combinatorics
Show that there exists a proper non-empty subset $S$ of the set of real numbers such that, for every real number $x$, the set $\{nx + S : n \in N\}$ is finite, where $nx + S =\{nx + s : s \in S\}$