Dianne Skoll wrote on 22/08/16 8:56 AM: > And... why can't a set contain itself? >
It can't in standard modern set theory (ZFC), through the foundation axioms, also known as the axiom of regularity https://en.wikipedia.org/wiki/Axiom_of_regularity which is a formulation that allows set theory to avoid Russell's Paradox. (see also https://en.wikipedia.org/wiki/ZFC) Just like Euclidean Geometry has the axiom that parallel lines never meet, and you get various non-euclidean geometries by changing that axiom, there are non-standard set theories that do not include the axiom of regularity, in which there can be sets that include themselves. None of that is relevant to the discussion of Marc Perkel's ideas because he is talking about sets of tokens from email (or sets of potential tokens?) not sets that contain sets. And all he needs to do with his infinite sets is be able to test if a token is in it, which is easy to do since the set is defined as the complement of a finite set. (I'm not saying this to agree with the method as good or to argue against it. I'm one of those people he mentions who understands how Bayesian spam filtering works who has yet to wrap my head around what he is presenting - For now I'm staying agnostic about it until I do understand it better). Sidney
