MathDB

An infinite set

S

of positive numbers is called thick, if in every interval of the form

\left [1/(n+1),1/n\right]

(where

n

is an arbitrary positive integer) there is a number which is the difference of two elements from

S

. Does there exist a thick set such that the sum of its elements is finite?
Proposed by Gábor Szűcs, Szikszó

A. 824