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 hpco...@hpcoders.com.au 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
