The Theory of Numbers as its name implies about numbers. Advanced Theory of Number is also about things like Elliptic Functions, Modular functions, Polynomials, Symmetry groups, the Riemann hypothesis.
What I am saying is I can express *ANY* numerical problem in binary form. I can use numbers, expressible in any base to define the above. Logic is in fact expressible if we take numbers of modulus 1, but that is another story. You do not have to express all of logic in terms of the Theory of Numbers. I am claiming that the Theory of Numbers, and all its advanced ramifications are expressible in terms of logic. - Ian Parker On 21 July 2010 21:01, Jim Bromer <jimbro...@gmail.com> wrote: > Because a logical system can be applied to a problem, that does not mean > that the logical system is the same as the problem. Most notably, the > theory of numbers contains definitions that do not belong to logic per se. > Jim Bromer > > On Wed, Jul 21, 2010 at 3:45 PM, Ian Parker <ianpark...@gmail.com> wrote: > >> But surely a number is a group of binary combinations if we represent the >> number in binary form, as we always can. The real theorems are those which >> deal with *numbers*. What you are in essence discussing is no more or >> less than the "*Theory of Numbers".* >> * >> * >> * - Ian Parker >> * >> On 21 July 2010 20:17, Jim Bromer <jimbro...@gmail.com> wrote: >> >>> I haven't made any noteworthy progress on my attempt to create a >>> polynomial time Boolean Satisfiability Solver. >>> I am going to try to explore some more modest means of compressing >>> formulas in a way so that the formula will reveal more about individual >>> combinations (of the Boolean states of the variables that are True or >>> False), through the use of "strands" which are groups of combinations. So I >>> am not trying to find a polynomial time solution at this point, I am just >>> going through the stuff that I have been thinking of, either explicitly or >>> implicitly during the past few years to see if I can get some means of >>> representing more about a formula in an efficient manner. >>> >>> Jim Bromer >>> *agi* | Archives <https://www.listbox.com/member/archive/303/=now> >>> <https://www.listbox.com/member/archive/rss/303/> | >>> Modify<https://www.listbox.com/member/?&;>Your Subscription >>> <http://www.listbox.com/> >>> >> >> *agi* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/> | >> Modify<https://www.listbox.com/member/?&;>Your Subscription >> <http://www.listbox.com/> >> > > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
