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Topic: computing k-th digit of a real number independently of the previous ones
Replies: 10   Last Post: Jul 1, 2012 4:12 PM

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 AMX Posts: 35 Registered: 8/22/09
Re: computing k-th digit of a real number independently of the
previous ones

Posted: Jun 24, 2012 3:32 PM

On Thu, 21 Jun 2012 14:29:09 -0700 (PDT),
angel.proorocu@gmail.com <angel.proorocu@gmail.com> wrote:

> Q: Is it possible to prove the existence of a real number with
> the property that in order to compute its k-th digit, we must
> compute all the previous ones?
>

This is not the property of the number, this is property of way
of computation (algorithm) and also representation of the number.

Consider x=1/3. LHS defines the real number (in some
representation). RHS defines how to compute x: divide 1 by 3. But
you can find a number of equivalent algorithms that gives as the
result 1/3. Their properties can be essentially different that
divison 1 over 3.

AMX

Date Subject Author
6/21/12 angel.proorocu@gmail.com
6/21/12 Gordon Sande
6/24/12 angel.proorocu@gmail.com
6/22/12 Martin Brown
6/24/12 angel.proorocu@gmail.com
6/24/12 AMX
6/25/12 Herman Rubin
6/27/12 AMX
6/27/12 Herman Rubin
6/30/12 AMX
7/1/12 Herman Rubin