On 8 Feb., 01:33, Virgil <vir...@ligriv.com> wrote:
> > You are in error again. There is the axiom of power set. For any F, > > there is P such that D e P if and only if D c F. According to it every > > subset of the countable set F exists. Will you dispute that the finite > > definitions of numbers are a subset of F? Not even the axiom of choice > > is required to prove that. > > A mere set of words, without even a specified order or grammar is not a > definition of anything. Thus your claim fails of its own idiocy.
The Axiom of Power Set For any set S, there exists a set P such that X e P if and only if X c= S. Original quote from Karel Hrbacek and Thomas Jech: "Introduction to Set Theory" Marcel Dekker Inc., New York, 1984, 2nd edition.