Why Has None of Computer Science been Formalized?
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From: Charlie-Boo on 18 Sep 2006 00:39 Steven Zenith wrote: > Charlie-Boo wrote: > > You are continuing to confuse abstract functions with concrete > > programs. Whether f(x) equals 2 or the square root of 2 is immaterial > > as far as functions are concerned. The function is defined in either > > case. The square root of 2 is a specific mathematical object, not a > > process that terminates or not. > > My apologies, I thought that you were talking about formalizing > computer science. > > In computer science the specification of such functions are constrained > by pragmatics. In computer science programs executing such functions > have desirable formal properties - termination is one of them. You said (about 10 times) that the function doesn't terminate. How do you define a function terminating? C-B > With respect, > Steven
From: Charlie-Boo on 18 Sep 2006 00:42 Steven Zenith wrote: > What do you plan to do with your arbitrary > precision value of root 2 when you have it? Are you going to use it in > an operation? If so, will you be able to maintain the specified > accuracy? Do you understand how to calculate real number arithmetic to an arbitrary number of decimal places? C-B > With respect, > Steven
From: Charlie-Boo on 18 Sep 2006 00:50 Steven Zenith wrote: > That root 2 does not terminate - is not computable - is an issue > in pure mathematics and the foundations of mathematics also since no > formula that uses the root of 2 is strictly computable. How about zero times the square root of 2? "Computable" refers to manipulating recursively enumerable sets (e.g. integers or character strings), not the real numbers. If one wants a program to derive properties of the square roots, then one would represent them as formulas (not infinite decimal expansions.) We can even write its value to any (finite) number of decimal places. You are confusing many basic concepts. C-B > Sincerely, > Steven
From: Charlie-Boo on 18 Sep 2006 01:05 zzbunker(a)netscape.net wrote: > Well, for the theorem even to make sense, > you have to define "all programming language" > better than just a recurive language. > Since that's nothing but Peano Axioms. What does that mean? > And you can easily prove that in the > Peano System, since it has no axioms of comphrension. Ok, prove it, please. "models of computation that have power equivalent to that of an idealized general purpose computer" - Bernard M. Moret "the capabilities of computers" - Michael Sipser "Turing Machines" - Dexter C. Kozen I formalize it as "a map from an r.e. set onto the set of recursive functions". Once again the published works do not really formalize concepts of Computer Science. C-B
From: Steven Zenith on 18 Sep 2006 03:13
Charlie-Boo wrote: > How about zero times the square root of 2? > > "Computable" refers to manipulating recursively enumerable sets (e.g. > integers or character strings), not the real numbers. > > If one wants a program to derive properties of the square roots, then > one would represent them as formulas (not infinite decimal expansions.) > We can even write its value to any (finite) number of decimal places. Since when is root 2 a real number? With respect, Steven |