> > There is no fixed number as cardinality. > > If we take the view that the naturals are an indefinite totality, > continually in the process of coming into being, it certainly makes > sense to say that the totality of finite initial segments of naturals > has no cardinality. It makes no sense whatever to insist it's finite.
That is a matter of taste. But it is not a matter of taste, whether or not we take this view. The other view, assuming complete infinite sets, is certainly contradicted by the requirement of two different Binary Trees which cannot be distinguished by nodes.