The Definition of Points
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From: PD on 15 Mar 2007 19:05 On Mar 15, 12:46 pm, Eckard Blumschein <blumsch...(a)et.uni- magdeburg.de> wrote: > On 3/14/2007 4:07 PM, PD wrote: > > > That's an interesting (but old) problem. How would one distinguish > > between continuous and discrete? As a proposal, I would suggest means > > that there is a finite, nonzero interval (where interval is measurable > > somehow) between successive positions, in which there is no > > intervening position. Unfortunately, the rational numbers do not > > satisfy this definition of discreteness, because between *any* two > > rational numbers, there is an intervening rational number. I'd be > > interested in your definition of discreteness that the rational > > numbers satisfy. > > Rational numbers are countable because all of them are different from > each other. > The two real numbers 0.9... and 1.0... with actually indefinite length > merely hypothetically exhibit a difference of value zero that tells us > the left one is nonetheless smaller than the right one. > > In other words: Real numbers must differ from rational ones by the > unreasonable claim of providing infinite acuity. IR just constitutes the > hypothetical border of the rationals. The continuum IS the tertium. > > Do not destroy this fortunate insight into how the border between number > and continuum works by stupid definitions. We need this heresy in order > to resolve several practical problems. > > Eckard Blumschein You did not answer my question about your definition of discreteness that rational numbers satisfy. Is being countable your definition of discreteness? PD
From: Lester Zick on 15 Mar 2007 19:15 On Thu, 15 Mar 2007 22:02:00 +0100, Ralf Bader <bader(a)nefkom.net> wrote: >Bob Kolker wrote: > >> Eckard Blumschein wrote: >>> >>> Rational numbers are countable because all of them are different from >>> each other. >> >> All real numbers are pairwise distinct but they constitute an >> uncountable set. >> >>> The two real numbers 0.9... and 1.0... with actually indefinite length >>> merely hypothetically exhibit a difference of value zero that tells us >>> the left one is nonetheless smaller than the right one. >> >> This is nonsense. Have you ever heard of a convergent series? >> >> 9/10 + 9/100 + etc converges to 1.0 > >Be warned - if you try to explain anything to Mr. Blumschein it will drive >you crazy. That's not a drive; it's a short putt. ~v~~
From: Lester Zick on 15 Mar 2007 19:20 On 15 Mar 2007 15:21:44 -0700, "Eric Gisse" <jowr.pi(a)gmail.com> wrote: >On Mar 15, 9:11 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On 14 Mar 2007 18:57:28 -0700, "EricGisse" <jowr...(a)gmail.com> wrote: >> >> >> >> >On Mar 14, 5:23 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> On 14 Mar 2007 14:54:55 -0700, "EricGisse" <jowr...(a)gmail.com> wrote: >> >> >> >On Mar 14, 11:15 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> >> On 13 Mar 2007 23:21:54 -0700, "EricGisse" <jowr...(a)gmail.com> wrote: >> >> >> >> >On Mar 13, 9:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> >> >> On 13 Mar 2007 17:18:03 -0700, "EricGisse" <jowr...(a)gmail.com> wrote: >> >> >> >> >> >On Mar 13, 9:52 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> >> >> >> The Definition of Points >> >> >> >> >> ~v~~ >> >> >> >> >> >> In the swansong of modern math lines are composed of points. But then >> >> >> >> >> we must ask how points are defined? However I seem to recollect >> >> >> >> >> intersections of lines determine points. But if so then we are left to >> >> >> >> >> consider the rather peculiar proposition that lines are composed of >> >> >> >> >> the intersection of lines. Now I don't claim the foregoing definitions >> >> >> >> >> are circular. Only that the ratio of definitional logic to conclusions >> >> >> >> >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> >> >> >> >> ~v~~ >> >> >> >> >> >Points, lines, etc aren't defined. Only their relations to eachother. >> >> >> >> >> So is the relation between points and lines is that lines are made up >> >> >> >> of points and is the relation between lines and points that the >> >> >> >> intersection of lines defines a point? >> >> >> >> >No, it is more complicated than that. >> >> >> >> Well that's certainly a relief. I thought you said "only their >> >> >> relations to each other". It's certainly good to know that what lines >> >> >> are made up of is not "only a relation" between points and lines. >> >> >> >> ~v~~ >> >> >> >No, I said "it is more complicated than that." >> >> >> No what you said is "Points, lines, etc aren't defined. Only their >> >> relations to eachother". Your comment that "No, it is more complicated >> >> than that" was simply a naive extraneous appeal to circumvent my >> >> observation that relations between points and lines satisfy your >> >> original observation. Your trivial ideas on complexity are irrelevant. >> >> >> ~v~~ >> >> >*sigh* >> >> >It isn't my fault you cannot read for comprehension. >> >> But it is your fault you cannot argue for comprehension by others. >> >> >Points and lines are undefined - it is as simple as that. >> >> Problem is that when you want to endorse an idea you say "it is as >> simple as that" and when you want to oppose an idea you say "it is >> more complicated than that" such that we have a pretty good idea what >> your opinions might be but no idea at all why your opinions matter or >> are what they are or should be considered true by others. >> >> > Every >> >question you ask that is of the form "So <idiotic idea> defines >> >[point,line]" will have "no" as an answer. >> >> So we should just accept your opinions as true without justification? >> Excuse moi but this is still a science forum and not merely a polemics >> forum. > >I gave a book suggestion [Sibley's geometry] and a Wikipedia link that >mirrors what is said in Sibley, plus I already explained that there >are undefined terms in geometry - and that 'point' is one of them. But a line made up of points is not one of them. >Why don't you just stop posting and leave science to those who are at >least marginally capable, unlike yourself? As you said, this is not a >polemics forum. Well I agree that unlike me you're only marginably capable of science. That's why I post to and for science while you're reduced to polemics. ~v~~
From: Lester Zick on 15 Mar 2007 19:26 On 15 Mar 2007 10:03:19 -0700, "VK" <schools_ring(a)yahoo.com> wrote: >On Mar 14, 11:02 pm, "PD" <TheDraperFam...(a)gmail.com> wrote: >> I believe Lester is asking whether a line is a composite object or an >> atomic primitive. > >That is one of things and the most easy one. I believe I already gave >the answer but not sure that he will ever accept it Oh I accept it all right. I just don't understand it. I always find it easier to accept things I don't understand. That's what philosophy and religion are for. Science is a little harder. It really helps to know whether and why things are true. Philosophy and religion just don't have much to say on the subject of truth. Their claims are many; their true demonstrations and explanations scarcer than hens' teeth. > : it is whatever >one wants it to be today thus whatever higher level constructs is one >planning to study. Sometimes for instance it is more benefitial to go >in definitions from surface rather than from point. The line then is >an intersection of two surfaces and the point is an intersection of >two lines. For the final touch it is left to define the surface as a >set of points and we are back to the round of circular definitions :-) >- but - in either case we don't care as we are getting the starting >point we need to move on. > >And - hidden for an appropriate moment - he also has an implicit join >of numbers and geometry, so number points and number lines are being >kept close to Euclidic points and lines for the next shot :-) > >And what he really wants I guess as a provable definition of a basic >abstraction. So he doesn't want a statement like "Got does exist" but >he wants a statement like "It is rainy today outside" so Lester could >just run outside to say is it true or not and provide his wet/dry >umbrella as an ultimate proof. > >So overall it is a rather demanding gentleman :-) I do the best I can. ~v~~
From: Bob Kolker on 15 Mar 2007 20:01
Eric Gisse wrote: > On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > > [...] > > What is your background in mathematics, Lester? You have asked: "what is the empty set". Bob Kolker > |