On Wednesday, December 11, 2013 11:35:55 AM UTC-7, WM wrote: > Am Mittwoch, 11. Dezember 2013 19:22:02 UTC+1 schrieb Zeit Geist: > > > > > The above Statement concerning FIS(d) does Not give us anything about d itself. > > > > And it does not refute my claim. > > > And your claim refutes nothing we have said. > > Fine for you. My claim says that by digits it is impossible to prove that d differs from all rational. That means up to every finite digit there are infinitely many rationals identical with d up to that digit. >
No, you use "up to every finite digit there are infinitely many rationals identical with d up to that digit." To show "by digits it is impossible to prove that d differs from all rational.".
This Does Not Follow.
> And if you acknowledge that d is nothing more than its digits, then there are infinitely many rational identical with d. >
But it is more. It is a certain arrangement of digits.
> And if you mention that d is more than its digits at finite places then you either need a digit at infinite place or a finite word defining some "structure". >
The structure is explicitly defined in the Axioms ( Properties) of the Real Numbers.
> > And all even numbers are divisible by 2. However this, as well as you above stament, have nothing to do with result of the Diagonalization Method. > > No this method, unles the result is defined by a finite word, does not accomplish what you thought or even think yet. >
Meaningless and Garbled.
> > > > Well, d is more than a Finite Set of Digits. Even if you All FIS(d) you don't have d; the "more" you speak of is Not its Digit, it is its Structure. > > > > You are wise. Why not apply that wisdom. The structure cannot be accounted for by digits. For that sake you need a finite word in the language that you wish to use. How many finite words are there in your language? > > > An Amount that can Not be put into a 1:1 correspondence with the Natural Numbers, > > Because it is too large or too less? >
Because, as others have said here, if you insist on Constructible Numbers, Functions and "Words" ( the Correspondence above is a Function ) only, There Is No 1:1 Function between the Set of "Words" and the Set of Natural Numbers.
> > And I don't need Digits, for they are simply Representations, and these Representations are Not Necessarily Faithful. > > But you would need digits or something else like that in order to "realize" uncountably many words. >
Which has nothing to do with "distinguishing by digits". Also, I don't need Digits to show the Uncountability of the Set of All Real Numbers.