The Definition of Points
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From: Tony Orlow on 31 Mar 2007 19:15 Lester Zick wrote: > On Fri, 30 Mar 2007 12:07:44 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>>> Those aren't geometrical expressions of addition, but iterative >>>>>> operations expressed linguistically. > >>>>> Which means what exactly, that they aren't arithmetic axioms forming >>>>> the foundation of modern math? The whole problem is that they don't >>>>> produce straight lines or colinear straight line segments as claimed. >>>> Uh, yeah, 'cause they're not expressed gemoetrically. >>> Well yes. However until you can show geometric expression are point >>> discontinuous I don't see much chance geometric expression will help >>> your case any. >>> >>> ~v~~ >> What does point discontinuity in geometry have to do with anything I've >> said? > > You talk about lines as if they were made up of points. > > ~v~~ I do, and the thread is picking up. And, that's not why. :) Or, maybe it is. No point lies independent of any space, or it's insignificant. No point is defined except as different in however many directions are under consideration. Where points are so defined, they allow for lines. :) 01oo
From: Tony Orlow on 31 Mar 2007 19:15 Lester Zick wrote: > On Fri, 30 Mar 2007 12:08:06 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>>> So, start with the straight line: > >>>>> How? By assumption? As far as I know the only way to produce straight >>>>> lines is through Newton's method of drawing tangents to curves. That >>>>> means we start with curves and derivatives not straight lines.And that >>>>> means we start with curved surfaces and intersections between them. >>>>> >>>> Take long string and tie to two sticks, tight. >>> Which doesn't produce straight line segments. >>> >>> ~v~~ >> Yeah huh > > Yeah indeed. > > ~v~~ I meant, "does, too". 01oo
From: Virgil on 31 Mar 2007 19:18 In article <460ee112(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > cbrown(a)cbrownsystems.com wrote: > > On Mar 31, 5:30 am, Tony Orlow <t...(a)lightlink.com> wrote: > >> Virgil wrote: > > > >>> In standard mathematics, an infinite sequence is o more than a function > >>> whose domain is the set of naturals, no two of which are more that > >>> finitely different. The codmain of such a function need not have any > >>> particular structure at all. > >> That's a countably infinite sequence. Standard mathematics doesn't allow > >> for uncountable sequences like the adics or T-riffics, because it's been > >> politically agreed upon that we skirt that issue and leave it to the > >> clerics. > > > > That's false; > > Please elucidate on the untruth of the statement. It should be easy to > disprove an untrue statement. TO claims politics is involved, but offers no proof, so that rejection of his claim as unproven is justified. TO claims religion is involved, but offers no proof, so that rejection of his claim as unproven is justified. > > > people have examined all sorts of orderings, partial, > > total, and other. The fact that you prefer to remain ignorant of this > > does not mean the issue has been skirted by anyone other than > > yourself. > > > > There have always been religious and political pressures on this area of > exploration. TO claims politics AND religion is involved, but offers no proof, so that rejection of his claim as unproven is justified. > > > > Yes, I left out some details. All of them, in fact.
From: Virgil on 31 Mar 2007 19:21 In article <460ee2bd(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460e5198(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <1175275431.897052.225580(a)y80g2000hsf.googlegroups.com>, > >>> "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >>> > >>>> On Mar 30, 9:39 am, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> > >>>>> They > >>>>> introduce the von Neumann ordinals defined solely by set inclusion, > >>>> By membership, not inclusion. > >>> By both. Every vN natural is simultaneously a member of and subset of > >>> all succeeding naturals. > >>> > >> Yes, you're both right. Each of the vN ordinals includes as a subset > >> each previous ordinal, and is a member of the set of all ordinals. > > > > In ZF and in NBG, there is no such thing as a set of all ordinals. > > In NBG there may be a class of all ordinals, but in ZF, not even that. > > > > > > No, that's true, The ordinals don't make a set. They're more like a mob, > or an exclusive club with very boring members, that forget what their > picket signs say, and start chanting slogans from the 60's. Whatever your on, TO, is undoubtedly illegal. For shame!
From: Tony Orlow on 31 Mar 2007 19:21
Virgil wrote: > In article <460e5899$1(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> stephen(a)nomail.com wrote: > >>> It is not even true in Tony's mathematics, at least it was not true >>> the last time he brought it up. According to this >>> definition {1, 2, 3, ... } is not actually infinite, but >>> {1, 2, 3, ..., w} is actually infinite. However, the last time this >>> was pointed out, Tony claimed that {1, 2, 3, ..., w} was not >>> actually infinite. >>> >>> Stephen >> No, adding one extra element to a countable set doesn't make it >> uncountable. > > Countability is a straw man. > yurnngghhh? ;o Virgule no sense making. > The issue is whether adding one element converts a > "not actually infinite" set into an "actually infinite" set. Of course it can't. It only adds one extra position to a sequence where all positions are finite, and a finite plus one more is still a finite, no? Which element can w come after in that set, in any order, which is in a finite position, and yet, has an infinite position immediately following it? Can't happen, can it? Nope, can't. I not to buy that. Tony |