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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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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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.


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