MathDB

Subset in The Form of Union of Segments

Source: 239 2004 S P6

May 15, 2020

algebra

Problem Statement

Do there exist a set

A\subset [0,1]

such that

(a)

A

is a finite union of segments of total length

\frac{1}{2}

(b)

The symmetric difference of

A

and

B:=A/2\cup(A/2+1/2)

is a union of segments of the total length less than

\frac{1}{10000}