On 4/4/2013 4:10 PM, Virgil wrote: > In article > <email@example.com>, > WM <firstname.lastname@example.org> wrote: > >>> No, a collection is no more and no less than "all its elements". >> >> But an inductive set contains elements that are not subject to >> induction? > > Only in Wolkenmuekenheim! >
Check the definitions.
The intersection of the class of all inductive sets containing the empty set is the inductive set for which every element has a finite chain of predecessors initiated with the empty set.
But, unlike WM, you are working from your stated definition which corresponds with a statement of the Dedekind-Peano axioms. I let myself get confused by all of this switching back and forth between "obvious" unstated theories.