Date: Dec 29, 2012 12:18 AM
Author: Virgil
Subject: Re: CHANGING THE DIAGONAL!
In article

<9533c4f1-686c-45be-8ef8-f7f4d3a9eab7@ui9g2000pbc.googlegroups.com>,

Graham Cooper <grahamcooper7@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 -

> >

> > > [1]

> > > you change each digit ONE AT A TIME

> > > 0.694...

> > > but this process NEVER STOPS

> >

> > > [2]

> > > 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.

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