Am Dienstag, 3. Dezember 2013 01:35:04 UTC+1 schrieb Virgil: > In article <firstname.lastname@example.org>, > > WM <email@example.com> wrote: > > > > > Am Montag, 2. Dezember 2013 20:27:15 UTC+1 schrieb Virgil: > > > > > > > > > > > > > > > What step produces the first undefinable number from a given set of > > > > > defined numbers? > > > > > > > > Undefineable numbers are not individually accessible, because > > > > individually accessible numbers are, by that very accessability, > > > > defineable. > > > > > > Fine, then undefinable numbers cannot result from any Cantor-argument - and > > > other theories do not contain them. So, why the heck do you think undefinable > > > numbers exist? > > Because WM claims that the set of definable numbers can be "counted", > > but Cantor has twice proved that the standard set of real numbers cannot > > be counted.
Producing a number that belongs to the countable set of producable numbers. Falsely interpreting that result as proof of uncountability. But he knew: Waere Koenigs Satz, dass alle ?endlich definirbaren" reellen Zahlen einen Inbegriff von der Maechtigkeit aleph_0 ausmachen, richtig, so hiesse dies, das ganze Zahlencontinuum sei abzaehlbar,
Today we know that Königs Satz is correct.
Every number that can be defined in English language so that Virgil and Zeit Geist know what is meant and are able to distinguish it from any other number - every such number belongs to the countable set of all defineable numbers.
Every uncountability-"proof" supplies a further defined number (or nothing at all). Therefore it is in principle impossible to prove something being uncountable. It is only possible to prove that something has *not yet* been counted. When, at the end of times, all Cantor-lists will have been constructed, they all will be counted. Further diagonalization is impossible, because time has ended - like every infinite Cantor-list "has an end".