Date: Dec 28, 2012 10:32 PM
Author: Graham Cooper
Subject: Re: CHANGING THE DIAGONAL!
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.

In this case, you cannot ANTI-DIAGONALISE an infinite set.

Every digit you change is substitutable by another digit in another

permutation.

Herc