An uncountable countable set
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From: Virgil on 26 Oct 2006 16:42 In article <4540d058$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <453faeb8(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > And even more puzzling, what does TO mean by "until t < 0"? > > > > Since "t < 0" is true before the experiment starts, TO must mean from > > the beginning of time. > > I mean during the interval [-1,0). Any less puzzled? Probably not. Still puzzled as to why TO said "until" an interval of time when he meant "during" that interval of time.
From: MoeBlee on 26 Oct 2006 16:48 Tony Orlow wrote: > I share your and Godel's concerns about point set theory Oh how rich. How veddy veddy scholarly Mr. Orlow sounds when he says such things, "I share Godel's concerns about point set theory." Too bad Mr. Orlow doesn't know a single ding dang thing about Godel, or Godel's concerns, or mathematical logic, or set theory, or point set topology, or topology. MoeBlee
From: Virgil on 26 Oct 2006 17:04 In article <4540d217(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <453fb285(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Mike Kelly wrote: > >>> Randy Poe wrote: > > > >>>> How is it, in your world, that when I specify times for all natural > >>>> numbered > >>>> balls, I am required to put in balls that don't have natural numbers? > >>> The problem is that Tony thinks time is a function of the number of > >>> insertions you've gone through. In order to "get to" any particular > >>> time you have to perform the insertions "up to" that point. He then > >>> thinks that if you want to "get to" noon, you have to have performed > >>> some "infinite" (whatever that means) iterations, where balls without > >>> natural numbers are inserted. That this is obviously not what the > >>> problem statement says doesn't seem to bother him. Nor that it's > >>> absolutely nothing like an intuitive picture of what time is. > >> Time is ultimately irrelevant in this gedanken, but if it is to be > >> considered, the constraints regarding time cannot be ignored. Events > >> occurring in time must occupy at least one moment. > > > > > > How is time irrelevant when every action is specified by the time at > > which it is to occur? > > Please specify the moment when the vase becomes empty. It IS empty at noon, but not before. But I do not know what TO means by "becomes". > > > > > The only relevant question is "According to the rules set up in the > > problem, is each ball inserted at a time before noon also removed at a > > time before noon?" > > > > An affirmative answer confirms that the vase is empty at noon. > > Not if noon is proscribed the the problem itself, which it is. How so? I see nothing in the statement of the problem which "proscribes" noon. > > > A negative answer directly violates the conditions of the problem. > > > > How does TO answer this question? > > > > As usual, he avoids such relevant questions in his dogged pursuit of the > > irrelevant. > > > > Noon does not exist in the experiment, or else you have infinitely > numbered balls. It is specifically mentioned in the experiment as the base time from which all actions are determined, so that if it does not exist then none of the actions can occur. If there is no noon then there can be no one minute before noon at which the first ball is inserted, so the vase is frozen in a state of emptiness. > > >>> Obviously, time is an independent variable in this experiment and the > >>> insertion or removal or location of balls is a function of time. That's > >>> what the problem statement says: we have this thing called "time" which > >>> is a real number and it "goes from" before noon to after noon and, at > >>> certain specified times, things happen. There are only > >>> naturally-numbered balls inserted and removed, always before noon. > >>> Every ball is removed before noon. Therefore, the vase is empty. > >> No, you have the concept of the independent variable bent. The number of > >> balls is related to the time by a formula which works in both directions. Where does the problem say that the numbers on balls being moved determines the time? > > > > As time is a continuum and the numbers of balls in the vase is not, > > there is no way of inverting the realtionship in the way that TO claims. > > Your times are as discontinuous as the number of balls, if no events can > happen at any other moments than those specified. That hardly means that there are no other times in between. Time is a continuum. Or does TO claim that time is quantized? > > >> So, when does the vase become empty? Nothing can occur at noon, as far > >> as ball removals. AT every time before noon, balls are in the vase. So, > >> when does the vase become empty, and how? > > > > The vase is empty when every ball has been removed, and that occurs at > > noon. > > So, that occurs AT noon? The vase becomes empty, when no balls are being > removed? Remember, every ball was removed BEFORE noon, and upon the > removal of each and every ball, more balls resided still in the vase. > So, how does the vase empty, when no balls are removed? So how is the vase be not empty after every ball is removed? > > >>> If you follow the sequence of insertions and removals you never "get > >>> to" noon but this doesn't imply that noon is never reached, or that > >>> iterations involving non-naturally numbered balls occur. It just > >>> implies that all insertion and removal is performed before noon. > >>> > >>> Tony won't let himself understand this. He is delusional. His problem. > >>> > >> I won't let myself accept self-contradictory conclusions. > > > > At least not unless they are TO's own personal self-contradictory > > conclusions. Like the existence of balls in a vase from which all balls > > have been removed. > > > > > > Like something occurring in time without at least a moment in which it > occurred. In the physical world, nothing happens instantaneously. In the mathematical world, pretty much everything does. In the mathematical world of the experiment, the balls move in and out of the vase instantaneously, and must be allowed to do so or the experiment cannot be performed at all. So either things can happen instantaneously or the experiment impossible. If TO allows a finite change of number of balls in the vase to occur instantaneously, what is so difficult about allowing an "infinite" change in the number of balls to occur instantaneously? TO seems to swallow camels and strain at gnats. > > TO's assumption that there must be a last ball removed in order for all > > balls to have been removed is part and parcel of his persistent delusion > > that there must be a last (finite) natural number in order to have a set > > of all (finite) natural numbers. > > No, that's what the problem implies when it claims to have completed the > sequence of naturals. The problem does not imply that to anyone except TO, so TO is still the only one claiming a "largest natural"
From: MoeBlee on 26 Oct 2006 17:04 Lester Zick wrote a post of such blazingly eminent intellectual depth, scope, imagination, and perspicacity that it would be mere pedantic and utterly petty captiousness of me to dispute, qualify, or even question a single word: > On 25 Oct 2006 17:47:15 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > > >> Yeah, Moe, look you do a lot of talking to justify one primitive. > > > >I'm not justifying a primitive. > > Well I'm glad you admit it. I was too polite to suggest it myself. > > >> My > >> primitive is "contradiction" or "differences" and I can justfy that as > >> true in one sentence. You say all your contentions "revert" (whatever > >> that may mean) to one "undefined non logical primitive" by which I > >> assume you mean one outright non demonstrable assumption > > > >No, I don't mean that. And I've already explained the difference. > > You have? Well thanks for the advisory anyway. > > > And > >again, since you are unfamiliar with even the most basic notions such > >as a primitive symbol, I'm pretty much wasting my time every time I > >write up explanations for you to receive in the lap of your own > >ignorance. > > Look who's talking about mis statements and mis characterization now, > Moe, not to mention outright character assassination.Cut to the quick. > > >> >No, primitives are individual symbols. > >> > >> So they're just symbolic assumptions of truth. > > > >No, they are very much NOT that. > > Then what are they, Moe? You're mighty long on flatout assertions when > it comes to what I say but mighty short on justifications when it > comes to what you say. > > >> >Yes, the term 'cardinality' is not in the above definition. > >> > >> So now if you don't say "cardinality" the concept isn't there? > > > >It just doesn't even work in the way you pose the question. I just > >can't explain how to do certain tasks on a computer to someone who > >won't even push the "on" button on the machine. I just can't explain > >how to regard mathematical defintions using mathematical logic to > >someone who just won't even read page one of a textbook. > > So now I can just add all this to the list of things you can't do but > have no problem criticizing in others when they criticize you for > things you can't do, can't justify, and can't explain. > > >> In other words if I can't intuit your faith based belief in standard > >> set analytical techniques you need to get back to the practice of your > >> religion and leave me to my own devices? > > > >No, my point is that I can't explain page 100 to you if you won't read > >page 1. > > And I can't explain truth to you if you insist that it's preferable to > assume the truth of your assumptions instead of demonstrating it. > > >Nor can I keep very interested in a conversation with someone such as > >you asks me questions on the subject but then replies to my answers > >with essentially, "Who asked you? Who cares?" > > Just trying to circumscribe the domain of ignorance with pointed > questions, Moe, when it comes to your complaining about things others > are ignorant of. Do you really expect anyone to research and document > for you the claims you make for modern math when you admit right up > front you can't justify their truth yourself? I mean if you can't even > be bothered to justify your opinions of a subject you claim to be > conversant with except by regression to other opinions about the same > subject, why would you expect others to take your claims seriously? MoeBlee
From: MoeBlee on 26 Oct 2006 17:06
Lester Zick wrote yet more analysis that just blows me away with its mathematical and rhetorical brilliance: > On 25 Oct 2006 14:41:53 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > >> So your arguments > >> for establishment views > > > >I am interested in learning ZF and related theories, but I do not claim > >that ZF is superior to any other theory. > > ZF and its kin are not theories because they can't be proven true. > They're only analytical methods. > > > In my arguments with cranks > > Ah yes the operative mathematically exhaustive definition for "crank" > being "crank(x)=disagree(u)". > > > I > >do not claim that ZF is the best theory (I have no opinion really on a > >"best theory", especially since at this stage I am just trying to > >learn, not make definitive normative judgments about "best"), > > Which is certainly wise when you have no idea whether your analytical > method is actually true. > > > but > >rather my points usually are to correct mistatements about what the > >actual formulations and theorems of set theory are, and to point out > >that the crank alternatives are not formal theories and not even within > >a thousand miles of being amenable to being a formal or EVEN coherent > >theory. > > Yes well you've certainly pointed that out on numerous occasions with > your own opinions as to what's what and when requested have even been > polite enough to back up those opinions with other opinions and when > all else failed have demanded people with differing opinions research > your opinions and document them for you. So what? Your virtue for what > it's worth is completely intact. > > >> It's all just a smoke > >> screen as far as I'm concerned, so much jargon and verbiage used to > >> simulate a sophisticated technical mathematical edifice where there is > >> none. > > > >And, since I have studied the subject, I know that you are wrong on > >that matter. The systems and terminology are given precisely (or can > >easily be made PERFECTLY precise with a bit of work on the reader's > >part, if perfect precision is required, as I do happen to require it of > >set theory). > > Yadayada whatever, Moe. More opinions to back up other opinions > followed by demands others research and justify your opinions for you. > > >You can claim a smoke screen all you want, but you won't even look at > >the actual performance of the mathematics you call a smoke screen. So > >of course, there is no possibility of convincing you that the system > >and terminology is precise. > > I never said it wasn't precise, Moe, I said precision didn't matter > when the issue was truth and the exhaustion of truth instead. What the > hell would the precision of pi mean if you're dealing with straight > lines instead of circular arcs. Precision is irrelevant if your > analytical technique is incorrect to begin with. > > > I could tell you that there exists a > >portable hard drive that carries more than a gigabyte in a device > >smaller than a pack of gum, and you can say forever that no such thing > >exists, since you won't even look at a showing of such a device. > > I'm only interested in your opinions to the extent the truth of your > opinions is demonstrable. You're opinions on math don't fall into the > same category because they aren't, you can't, and you're perfectly > content with the assumption of truth instead. That's the difference. > > > I can > >say that set theory is a completely rigorous system that axiomatizes > >the usual theorems of real analysis, and you can say forever that it is > >not rigorous, just a smoke screen, forever, since you won't read a book > >that shows just such a rigorous axiomatization. > > You mean I won't research and justify your opinions for you on your > sayso when you can't even begin to do it for yourself? Why bother? > > ~v~~ MoeBlee |