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Topic: CHANGING THE DIAGONAL!
Replies: 6   Last Post: Dec 29, 2012 4:14 AM

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Virgil

Posts: 6,990
Registered: 1/6/11
Re: CHANGING THE DIAGONAL!
Posted: Dec 29, 2012 12:18 AM
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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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