The Definition of Points
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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 >
From: Eric Gisse on 16 Mar 2007 00:15 On Mar 15, 4:01 pm, Bob Kolker <nowh...(a)nowhere.com> wrote: > 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". The empty set was my only source of amusement in my proofs class. > > Bob Kolker > >
From: Brian Chandler on 16 Mar 2007 03:46 Lester Zick wrote: > On Wed, 14 Mar 2007 22:30:21 +0100, "SucMucPaProlij" > <mrjohnpauldike2006(a)hotmail.com> wrote: > > >> If the point is defined by the intersection what happens to the point > >> and what defines the point when the lines don't intersect? > >> On the other hand if the point is not defined by the intersection of lines > >> how can one assume the line is made up of things which aren't defined? > >> > > > >hahahahaha you are poor philosopher. > > Obviously. That's why I became a mathematician. You did? Gosh, congratulations! Brian Chandler http://imaginatorium.org (just wanting to be part of this golden thread, this irridescent braid, this)
From: Eckard Blumschein on 16 Mar 2007 04:52
On 3/16/2007 12:05 AM, PD wrote: > You did not answer my question about your definition of discreteness > that rational numbers satisfy. Is being countable your definition of > discreteness? What we are calling definition is usually the attempt to pinpoint something by means of a non-circular description. Why should I define discreteness of something by saying it is uncountable? If so, wouldn't the relationship be valid the other way round too? I would rather like to state that there is a fundamental property which utters itself in that ... and in that... . What about countability, we have to anticipate the mistake that it is so far merely understood like a property of a set. Incidentally, Cantor himself used the word countable in the sense 'there is a bijection to the naturals' while he used "counted" (abgezaehlt) in the common sense meaning. I say, already the decimal representation of the unresolvable task called pi is uncountable. In my understanding even 0.99... is an uncountable representation. Any number is uncountable if only existing or just embedded in IR. Embedded rationals are uncountable as long as they do not belong to Q but to IR. Is this too strange to you? Eckard Blumschein |