On 7/5/07, Raul Miller <[EMAIL PROTECTED]> wrote:
On 7/5/07, Terrence Brannon <[EMAIL PROTECTED]> wrote:
> So, likewise, learning J should be like following a proof in a > textbook, right? What kind of proof? If I recall correctly, we tend to ask students to study a variety of mathematical concepts for years (and try to ensure they get a robust practical background in some of those topics) before we ask them to understand the simplest of proofs.
yes and because so many people are no good at math, there's clearly something wrong with this approach.
> But then again, math is limited by Goedel's Incompleteness > theorem whereas computers can do more? That does not match my understanding, of Goedel's Incompleteness theorem, nor of the character of computers. As I understand the incompleteness theorem: a mathematical system of sufficient complexity will allow an infinite number of statements which are not resolvable simply by recourse to previous axioms (definitions).
Actually, your statement refers to half of what I understand about that theorem. A mathematical system can be either complete, or correct, but not both. You are talking about a correct system which is not complete above. The other possibility is to have a complete system which is not correct. But my understanding of that theorem is limited to Hofstadter's (brilliant!) book and nothing more. -- J IRC Channel irc://irc.freenode.org/jsoftware ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
