Prove that every partition of
-dimensional space into three disjoint subsets has the following property: One of these subsets contains all possible distances; i.e., for every
, there are points
and
inside that subset such that distance between
and
is exactly
%V0
Prove that every partition of $3$-dimensional space into three disjoint subsets has the following property: One of these subsets contains all possible distances; i.e., for every $a \in \mathbb R^+$, there are points $M$ and $N$ inside that subset such that distance between $M$ and $N$ is exactly $a.$
Školjka