The Definition of Points
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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
From: Lester Zick on 31 Mar 2007 20:13 On Fri, 30 Mar 2007 12:33:00 -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: >> >>>> If I don't seem particularly interested in demonstrations of universal >>>> truth it's partly because you aren't doing any and I've already done >>>> the only ones which can matter. It's rather like the problem of 1+1=2 >>>> or the rac trisection of general angles. Once demonstrated in reduced >>>> mechanically exhaustive terms the problem if not its explication and >>>> implications loses interest. If you want to argue the problem itself >>>> go ahead. Just don't expect me to be interested in whether 1+1=2 or >>>> whether you can trisect general angles. >>> You assume OR in defining AND, and then derive OR from AND, all the >>> while claiming all you've done is NOT. >> >> Of course I do. That's specifically why I chose to specify (A B) so I >> could get around the presence of conjunctions like "or" which I didn't >> know were there but I'll take your word for it since you seem to know >> and say what's there and what's not without having to demonstrate it >> whereas I'm forced to demonstrate what I say even though you don't. So >> I suppose we can just assume (A B) means there's a conjunction >> involved on your per say without having to demonstrate its presence. >> >> ~v~~ > >Okay, fill in this table for me please, explaining whether (A B) is true >or false in the following circumstances: What table, Tony? What true false? >A B (A B) >true true true or false? >true false true or false? >false true true or false? >false false true or false? > >Now, we can see what 2-place operator you're talking about. What two place operator, Tony? Would you care to define any of these terms before talking about them or should we try to talk about them before defining them? I don't mind talking about tables, true, false, two place operators, etc. before defining them but then I insist on my definitions intead of yours. Of course I can't tell exactly what my definitions might be until I define them in preference to yours. But that doesn't really matter since they're my definitions to begin with. ~v~~
From: Tony Orlow on 31 Mar 2007 20:14
Virgil wrote: > In article <460ee48e(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > >> Why? What have I defined, if not a sequence? Is there a word for it? It >> must "exist", if I assert so. > > Does TO now claim the right of God to make things exist by His command? > > I understand that God is a jealous God, and takes such usurpations in > very bad part. I claim equal right to use existential instantiation. Tony |