Am I a crank?
in [Math]
|
Prev: Any coordinate system in GR?
Next: Euclidean Spaces
From: Han de Bruijn on 31 Aug 2006 03:29 Virgil wrote: > In article <c0kbf2d68q0iembtij08v9763k92e59fmt(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >>On Wed, 30 Aug 2006 09:10:10 +0200, Han de Bruijn >><Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> >>>Axioms are implicit definitions. > > Axioms are not at all definitions, nor are definitions axioms. > Axioms are declarative, definitions imperative. Don't see the difference. The axioms of planar Euclidian geometry IMHO are an implicit definition of what you can do and cannot do with points and straight lines, i.e. what they _are_ in a mathematical sense. Han de Bruijn
From: Han de Bruijn on 31 Aug 2006 03:34 Virgil wrote: > Let's see Zick empirically establish the axiom of infinity, then. Nobody can. Therefore it does not correspond to (part of an) implicit definition of some real world thing. Therefore it will do no harm if we throw it out. Han de Bruijn
From: Proginoskes on 31 Aug 2006 03:41 schoenfeld.one(a)gmail.com wrote: > Proginoskes wrote: > > schoenfeld.one(a)gmail.com wrote: > > > Han de Bruijn wrote: > > > [...] > > > > Or is it just mathematics? In the latter case, computing a large prime > > > > is also mathematics, because it could be done - in principle - by hand. > > > > (What else does computer science add except more speed and more space.) > > > > > > Then there is no experiementation. Mathematics is not an experimental > > > science, it is not even a science. The principle of falsifiability does > > > not apply. > > > > Written by someone who has not done any math research. > > > > One of many examples: Try dividing 2^n by n and keeping track of the > > remainders. You won't get 1; you get 2 a lot, but you never seem to get > > a 3. So you conjecture: > > > > CONJECTURE: The remainder of 2^n divided by n is never 3. > > > > However, this conjecture is false; in particular, the remainder of 2^n > > divided by n is 3 if n = 4,700,063,497 (but for no smaller n's). > > Hello Crackpot. I did _not_ concoct this example; it's from one of Richard K. Guy's "Strong Law of Small Numbers" papers. If you don't believe it, find a smaller n. --- Christopher Heckman
From: Proginoskes on 31 Aug 2006 03:45 Virgil wrote: > In article <bn4cf213is70kjhmu35h9e7945hc3bb36i(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > > > On Wed, 30 Aug 2006 13:43:02 -0600, Virgil <virgil(a)comcast.net> wrote: > > > > >In article <r7kbf2tlc70iqjm2rp4ktprl1o3uui79jf(a)4ax.com>, > > > Lester Zick <dontbother(a)nowhere.net> wrote: > > > > > > > > >> >Hello Crackpot. > > >> > > >> Crackpot=disagreer. Quite mathematical. > > > > > >Crackpots are those who disagree not only without supporting evidence > > >but despite contrary evidence. > > > > > >Like Zick. > > > > Like exactly what contrary evidence do you mean, sport? Your opinions > > and assumptions of what's true and false? Or in your case I guess I > > should say your opinion of what's not true and not false? > > Zick claims that mathematicians claim their axioms to be true. Like I pointed out, the example I gave depends only on elementary-school arithmetic, and if the statement is false, it should be easy to show. The statement in question was: The remainder of 2^n when divided by n is 3 when n = 4,700,063,497 but false for any smaller values of n. This was not done off the top of my head; it's an example from one of Richard K. Guy's "Strong Law of Small Numbers" papers, and was proven by Lehmer and Lehmer. --- Christopher Heckman
From: Virgil on 31 Aug 2006 04:21
In article <4f27f$44f68fcd$82a1e228$17921(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <c0kbf2d68q0iembtij08v9763k92e59fmt(a)4ax.com>, > > Lester Zick <dontbother(a)nowhere.net> wrote: > > > >>On Wed, 30 Aug 2006 09:10:10 +0200, Han de Bruijn > >><Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >> > >>>Axioms are implicit definitions. > > > > Axioms are not at all definitions, nor are definitions axioms. > > Axioms are declarative, definitions imperative. > > Don't see the difference. The axioms of planar Euclidian geometry IMHO > are an implicit definition of what you can do and cannot do with points > and straight lines, i.e. what they _are_ in a mathematical sense. Axioms are about how the objects of a system interrelate. Definitions are no more than abbreviations like "Let 'A' stand for 'B'". E.g., "let 'triangle' stand for a set of 3 non-colinear points together with three line segments joining them in pairs". |