Axiom talk:Axiom of Foundation

Definition of Founded
As it stands, the sentence: "The membership relation is founded on any set." needs to be explained, as the term "founded" has not been defined. Presumably it is the same as well-founded, in which case a link to that definition is in order. However, in that case a link needs to be made to the proof which defines the equivalence of an ordering and the subset relation (somewhere in Category:Ordinals, which needs to be looked at very carefully to ensure there is nothing circular going on.)

In any case, something needs to be said about "founded" being defined as being "like what this axiom says". At the moment it's just an undefined term. --prime mover 16:32, 8 September 2011 (CDT)

Well, it is the the same thing as a well-founded relation if we take the definition given by Wikipedia [] (external) - see the fifth bullet under "Examples". However, it apparently does not match the definition of well-founded relations given here, because the membership relation is not a poset (if I understand correctly, then a partial ordering is one that is reflexive, transitive, and antisymmetric). --asalmon 8 September 2011