On Thu, 21 Jun 2012 14:29:09 -0700 (PDT), email@example.com <firstname.lastname@example.org> 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.