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Topic: Bizarritudes
Replies: 101   Last Post: Jul 31, 2005 9:05 PM

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 fernando revilla Posts: 683 From: Madrid Registered: 5/25/05
Re: Bizarritudes
Posted: Jul 27, 2005 3:43 PM

> > bischar <bisch_a_r@yahoo.fr> writes in article
> >

> <13842344.1122478023914.JavaMail.jakarta@nitrogen.math
>

> > forum.org> dated Wed, 27 Jul 2005 11:26:33 EDT:
> > >Would there be a function that would extract
> precise
> > digits and create a new number with them ?
> > >
> > >I mean a function that would make from pi

> > 3.04050205050909
> >
> >02080606030802090008040901090903050008000709040903070

>
> > 10406
> > >08020809060803080504010706 and
> > 0.1010906030807030304020403
> >
> >03070502080107060309070105020904040502000806000206000

>
> > 90802
> > >000402030201000 for instance.
> >
> > Anything which you can descibe in such a way that
> > f(x) is unambiguous
> > is a function. In the above case, you would

> define
> > f:R -> R^2, because
> > there are two different output values.
> >
> > The one caveat I see in your definition is that
> > f(.999999...) != f(1.0).
> > Unless you fix this, it's not exactly a function

> on
> > reals but on digits.
> >

> > >Or another function that would insert a zero
> between
> > all the digits composing the initial number ?
> >
> > Same problem with .99999...
> >
> > --Keith Lewis klewis {at} mitre.org
> > The above may not (yet) represent the opinions of

> my
> > employer.
>
> And what would a 'function on digits' look like ?

Bischar, I have the solution for all your problems:

1.- Consider the bijectve function f : R+ -> [0,1)

f( x )= (2/pi) arctan x

2. Consider the dynamical system x_(k+1)=frac(2x_k), which
will allow you to set out a binary codification of [0, 1) by means
of O^+(y) ( orbit of y = f ( x ) ).

3.- Now, for every x>=0 you have a "nice" expression for x.

The problem is, there will be your computer screen so big
for showing the results ?

Date Subject Author
7/16/05 bischar
7/16/05 bischar
7/16/05 bischar
7/16/05 bischar
7/16/05 bischar
7/16/05 bischar
7/16/05 bischar
7/17/05 bischar
7/19/05 Gerry Myerson
7/19/05 bischar
7/19/05 Gerry Myerson
7/19/05 bischar
7/20/05 John Ramsden
7/20/05 bischar
7/23/05 bischar
7/23/05 bischar
7/23/05 Jim Burns
7/23/05 bischar
7/24/05 Jim Burns
7/24/05 bischar
7/24/05 Jim Burns
7/24/05 Proginoskes
7/24/05 Robert Israel
7/24/05 bischar
7/25/05 Jim Sprigs
7/25/05 bischar
7/25/05 Proginoskes
7/25/05 bischar
7/23/05 bischar
7/23/05 bischar
7/23/05 bischar
7/25/05 bischar
7/25/05 Robert Israel
7/25/05 bischar
7/25/05 Rick Decker
7/25/05 bischar
7/25/05 Robert Israel
7/25/05 bischar
7/25/05 bischar
7/25/05 bischar
7/26/05 Robert Israel
7/26/05 bischar
7/26/05 Robert Israel
7/26/05 bischar
7/25/05 bischar
7/25/05 bischar
7/26/05 bischar
7/26/05 Proginoskes
7/26/05 bischar
7/26/05 bischar
7/26/05 bischar
7/26/05 bischar
7/26/05 Gerry Myerson
7/26/05 bischar
7/26/05 Gerry Myerson
7/26/05 bischar
7/27/05 Gerry Myerson
7/27/05 quasi
7/27/05 bischar
7/27/05 Robert Israel
7/27/05 bischar
7/27/05 Dik T. Winter
7/27/05 bischar
7/26/05 bischar
7/27/05 bischar
7/27/05 fernando revilla
7/27/05 bischar
7/27/05 Keith A. Lewis
7/27/05 bischar
7/27/05 fernando revilla
7/27/05 bischar
7/27/05 fernando revilla
7/27/05 bischar
7/27/05 bischar
7/28/05 bischar-
7/28/05 bischar-
7/28/05 bischar
7/28/05 Timothy Little
7/28/05 bischar
7/29/05 The Ghost In The Machine
7/28/05 bischar
7/28/05 bischar
7/28/05 quasi
7/28/05 bischar
7/28/05 quasi
7/28/05 bischar
7/28/05 bischar
7/28/05 bischar
7/29/05 fernando revilla
7/29/05 bischar
7/29/05 bischar
7/29/05 bischar
7/29/05 Robert Israel
7/29/05 bischar
7/31/05 Gerry Myerson
7/29/05 bischar
7/29/05 Robert Israel
7/29/05 bischar
7/29/05 bischar
7/29/05 Robert Israel
7/30/05 bischar
7/30/05 bischar