Sorry - I believe I am off topic as this is not relevant given: "This indirectly enforces the idea that sets cannot have duplicate elements, as set membership

Sorry - I believe I am off topic as this is not relevant given: "This indirectly enforces the idea that sets cannot have duplicate elements, as set membership is defined purely by the presence or absence of elements. For example:" So there is a constraint on what sort of trees are allowed in this -forrest- which would preclude most finite rooted trees.