Despite several negative comments, I thought the author did a great job of explaining and playing with set theory (which, as can be seen by the response, is good fun.)

I do take some issue with intepreting set theory's membership relation in terms of the tree child relation, though.

First, the child relation is presumably transitive, whilst set membership is not. (The subset relation is transitive. Presumably it is 'direct child' relation we have in mind here.)

Second, as seen in the third diagram, nodes don't map well to set entities, because the same entity can be a member of distinct sets, but these would count as distinct nodes on some trees. E.g., in the diagram both leaf nodes are distinct, but they both represent the empty set, and hence should be identical. So the identity of sets is not preserved in the tree encoding.

But this is picky — a lovely read. Thanks author!