In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 3 May 2014 20:55:10 UTC+2, Virgil wrote: > > > > > You have not shown an undefinable object. > > > > > But I have shown the necessity for them. > > No. We have the fact that in set theory the set of definable numbers is > uncountable by the fact that it cannot be listed and is countable by the fact > that all finite expressions, expressing numbers, relations, functions, > mathematicians, and nonsense, form a countable set.
Only if one assumes that every real number must have an individual definition in order to exist even as an individually undefineable member of defineable set, but that has repeatedly been proved false. At least everywhere outside of WM's wild weird world of WMytheology. > > You cannot avoid this contradiction.
I, and other mathematicians already have have avoided it and mathetmaics as a whole has avoided it by allowing the set of all subsets of a given set to be collectively defineable without requiring each of those subset to be individually defineable.
That WM keeps denying this obvious mathematical fact is only one of his many mathematical delusions. --