MathDB

set {nx + S : n \in N}$ is finite, where nx + S ={nx + s : s \in S}

Source: Danube 2013 p4

July 22, 2019

Setsset theorycombinatorics

Problem Statement

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\}