Let S be the set of all polygonal areas in a plane. Prove that there is a function f:S→(0,1) which satisfies f(S1∪S2)=f(S1)+f(S2) for any S1,S2∈S which have common points only on their borders
Source: Romania IMO TST 1991 p4
Tags: function, combinatorial geometry, geometry
Let S be the set of all polygonal areas in a plane. Prove that there is a function f:S→(0,1) which satisfies f(S1∪S2)=f(S1)+f(S2) for any S1,S2∈S which have common points only on their borders