The Definition of Points
in [Math]
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From: Lester Zick on 31 Mar 2007 20:06 On Fri, 30 Mar 2007 12:31:08 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <460d489b(a)news2.lightlink.com>, > 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: >> > >> >>> Just ask yourself, Tony, at what magic point do intervals become >> >>> infinitesimal instead of finite? Your answer should be magnitudes >> >>> become infintesimal when subdivision becomes infinite. >> >> Yes. >> > >> > Yes but that doesn't happen until intervals actually become zero. >> > >> >> But the term >> >>> "infinite" just means undefined and in point of fact doesn't become >> >>> infinite until intervals become zero in magnitude. But that never >> >>> happens. >> >> But, but, but. No, "infinite" means "greater than any finite number" and >> >> infinitesimal means "less than any finite number", where "less" means >> >> "closer to 0" and "more" means "farther from 0". >> > >> > Problem is you can't say when that is in terms of infinite bisection. >> > >> > ~v~~ >> >> Cantorians try with their lame "aleph_0". Better you get used to the >> fact that there is no more a smallest infinity than a smallest finite, >> largest finite, or smallest or largest infinitesimal. Those things >> simply don't exist, except as phantoms. > >But all other mathematical objects are equally fantastic, having no >physical reality, but existing only in the imagination. So any statement >of mathematical existence is always relative to something like a system >of axioms. Whew. Means you don't have to consider whether they're true. Quite a relief I'd say. You can always take it up with someone who unlike yourself isn't too lazy or stupid to think for a living. ~v~~
From: Mike Kelly on 31 Mar 2007 20:06 On 1 Apr, 00:58, Tony Orlow <t...(a)lightlink.com> wrote: > step...(a)nomail.com wrote: > > In sci.math Brian Chandler <imaginator...(a)despammed.com> wrote: > >> step...(a)nomail.com wrote: > >>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>> If all other elements in the sequence are a finite number > >>>> of steps from the start, and w occurs directly after those, then it is > >>>> one step beyond some step which is finite, and so is at a finite step. > >>> So you think there are only a finite number of elements between 1 and > >>> w? What is that finite number? 100? 100000? 100000000000000000? > >>> 98042934810235712394872394712349123749123471923479? Which one? > > >> None of the ones you've mentioned. Although it is, of course, a > >> perfectly ordinary natural number, in that one can add 1 to it, or > >> divide it by 2, its value is Elusive. Only Tony could actually write > >> it down. > > > These Elusive numbers have amazing properties. According to > > Tony, there are only a finite number of finite naturals. > > There exists some finite natural Q such that the set > > { 1,2,3,4,.... Q} > > is the set of all finite natural numbers. But what of Q+1? > > Well we have a couple of options: > > a) Q+1 does not exist > > b) Q+1 is not a finite natural number > > c) { 1,2,3,4, ... Q} is not the set of all finite natural numbers > > > Tony rejects all these options, and apparently has some fourth > > Elusive option. > > > Stephen > > Oy. The "elusive" option is that there is no acceptable "size" for N. > That was really hard to figure out after all this time... Lucky, then, that set theory don't refer to the "size" of sets but rather to their "cardinality". You still haven't figured that out after all this time. It's a very strange mental block to have. -- mike.
From: Tony Orlow on 31 Mar 2007 20:09 Virgil wrote: > In article <460ee056(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> stephen(a)nomail.com wrote: >>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > >>> If all you mean by "actually infinite" is "uncountable", then >>> just say "uncountable". Of course an "uncountable sequence" >>> is a contradiction, so you still have to define what you mean >>> by a "sequence". >>> >>> >> Please do expliculate what the contradiction is in an uncountable >> sequence. What is true and false as a result of that concept? > > A mathematical sequence is a function with the naturals as domain. > If TO wishes to refer to something which is not such a function, he > should not refer to it as a sequence if he wishes to be understood in > sci.math. > > Pray tell, what term shall I use???? >>> I know you are incapable of actually thinking about all the elements of N, >>> but that is your problem. In any case, N is not an element of N. >>> Citing Ross as support is practically an admission that you are wrong. >>> >>> Stephen >>> >> Sure, of course, agreeing with someone who disagrees with you makes me >> wrong. I'll keep that in mind. Thanks.. > > It is not so much that Ross disagrees with one person, it is that he > disagrees with everyone, frequently including himself. Ross has a vision, even if not axiomatically expressed. In fact, he's entirely honest about that, expounding an axiom free system. I like Ross. So do you. Admit it. :) Tony Orlow Orlonics.net ;)
From: Tony Orlow on 31 Mar 2007 20:11 Virgil wrote: > 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. I feel so rejected.... (sniff) Tony
From: Tony Orlow on 31 Mar 2007 20:12
Virgil wrote: > 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! What I have in my possession is only a minor violation in this state, and it's ridiculous to make a plant illegal anyway, especially one with so many ties to human progress and insight. Tony |