On Wed, Jan 22, 2014 at 11:12:50AM +0100, Bruno Marchal wrote: > > > A set (of natural numbers) is creative if > 1) it is RE (and thus is some w_k) > 2) its complement (N - w_k) is productive, and this means that for > all w_y included in, we can recursively (mechanically) find an > element in it, not in W_y. > > It means that the set is RE and his complement is constructively NOT > RE. Each attempt to recursively enumerate he complement can be > mechanically refuted by showing explicitlky a counterexample in it, > and this gives the ability to such a creative set to approximate its > complement in a transfinite progressions of approximation. this > gives an ability to jump to a bigger picture out of the cuurent > conception of the big picture. I find it a reasonable definition of > creativity. >
Yes - I recall that was how the Wikipedia article defined it. But I don't grok it. What is the motivation for such a definition? What about some examples (I'm guess the Mandelbrot set might be one such)? > The John Myhill proved that a set is creative iff it is Turing > complete, i.e. Turing universal. > So that RE set > What is a Turing complete _set_? -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
