MathDB

Show that any two intervals

A, B\subseteq \mathbb R

of positive lengths can be countably disected into each other, that is, they can be written as countable unions

A=A_1\cup A_2\cup\ldots\,

and

B=B_1\cup B_2\cup\ldots\,

of pairwise disjoint sets, where

A_i

and

B_i

are congruent for every

i\in \mathbb N

[Gy. Szabo]

Problem Statement