On Dec 29, 3:18 pm, Virgil <vir...@ligriv.com> wrote: > In article > <9533c4f1-686c-45be-8ef8-f7f4d3a9e...@ui9g2000pbc.googlegroups.com>, > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > > > On Dec 29, 11:37 am, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <adde38fa-1e63-43a1-94f0-908da37a4...@s6g2000pby.googlegroups.com>, > > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > +-----> > > > > | 0. 542.. > > > > | 0. 983.. > > > > | 0. 143.. > > > > | 0. 543.. > > > > | ... > > > > v > > > > OK - THINK - don't back explain to me. > > > > You run down the Diagonal 5 8 3 ... > > > > IN YOUR MIND - > > > > >  > > > > you change each digit ONE AT A TIME > > > > 0.694... > > > > but this process NEVER STOPS > > > > >  > > > > so you NEVER CONSTRUCT A NEW DIGIT SEQUENCE! > > > > That is like saying that the function f+ |N -> |N : x \_--> x^2 > > > never ends. > > > Right! but since it has no free variable input to apply it's safe to > > extrapolate results toward infinity. > > > > As soon as one has a completed rule by which values of the function are > > > determined from its domain to its codomain, the function is defined. > > > > E.g., f:|N --> |N : 2 |--> 2*x+1 > > > is completed function > > > > Thus a rule or function for determining anti-diagonal digits creates the > > > entire anti-diagonal list of digits in one step. > > > dependent on the input. > > As a function of the input certainly, but one theat function is defined > the process is essentially completed. > > > > > In this case, you cannot ANTI-DIAGONALISE an infinite set. > > > Every digit you change is substitutable by another digit in another > > permutation. > > I have defined a function which does it automatically for any and every > list of endless sequences of decimal digits, giving a resulting sequence > not listed in that list. >
It has a parameter that only works given LIST format.
It doesn't prove a SET of reals is in-complete.
Here is the SET of all reals.
UTM( real , digit ) [mod 10]
that is a complete specification of the set.
However, there are infinitely many permutations, due to there being infinitely many universal turing machines in infinitely many different languages.
Since your process has a free variable, the never ending cross- sequence you compute is dependent on your own selected free variable, the permutation you must select for listable format for your process to work.
IF you got out of your corner and examined the other methods put forth you would see this.
IS 0. T(2,1) T(1,2) T(3,3) T(4,4) ...
absent from L?
T is the list of all reals with the digit changing function applied to all digits of every real.
If you cannot address the posts in the group you should stop yourself from arguing against them.