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

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Graham Cooper

Posts: 4,293
Registered: 5/20/10
Re: CHANGING THE DIAGONAL!
Posted: Dec 28, 2012 10:32 PM
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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




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