An uncountable countable set
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From: David Marcus on 26 Oct 2006 18:31 stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > stephen(a)nomail.com wrote: > >> As someone else has pointed out, the "balls" and "vase" > >> are just an attempt to make this sound like a physical problem, > >> which it clearly is not, because you cannot physically move > >> an infinite number of balls in a finite time. It is just > >> a distraction. As you say, the problem originates in mathematics. > >> Any attempt to impose physical constraints on inherently unphysical > >> problem is just silly. > >> > >> The problem could have been worded as follows: > >> > >> Let IN = { n | -1/(2^floor(n/10) < 0 } > >> Let OUT = { n | -1/(2^n) } > > > I think you meant > > > Let OUT = { n | -1/(2^n) < 0 } > > >> What is | IN - OUT | ? > >> > >> But that would not cause any fuss at all. > > > I wonder. Does anyone reading this think | IN - OUT | <> 0? > > Tony does. Apparently so. I wonder if he would have thought that if he hadn't first read the balls and vase problem. -- David Marcus
From: Lester Zick on 26 Oct 2006 18:35 On 26 Oct 2006 14:06:11 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote > >yet more analysis that just blows me away with its mathematical and >rhetorical brilliance: Well obviously it blows you away with its rhetorical brilliance or you wouldn't bother to front post. As to its mathmatical significance I'll grant you its brilliance. As to its jazz significance I couldn't be bothered to say. >> 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~~
From: Virgil on 26 Oct 2006 18:39 In article <MPG.1fab004d7cfbeaf0989778(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Virgil wrote: > > In article <4540d217(a)news2.lightlink.com>,Tony Orlow <tony(a)lightlink.com> > > wrote: > > > > > 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. > > That's a good point. > > > > 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? > > That's another good point. However good they may be, I have a feeling that TO will find a way of ignoring them .
From: Dik T. Winter on 26 Oct 2006 19:19 In article <1161829100.130312.44340(a)i42g2000cwa.googlegroups.com> "Ross A. Finlayson" <raf(a)tiki-lounge.com> writes: > Dik T. Winter wrote: > > In article <1161825225.141821.66550(a)e3g2000cwe.googlegroups.com> "Ross A. Finlayson" <raf(a)tiki-lounge.com> writes: > > ... > > > Cardinals are ordinals and in a set theory: sets. > > > > > > Generally it's known that you get cardinals from the previous using the > > > powerset operation, > > > > Through what powerset operation do you get the cardinal 3? > > > > > and ordinals from the previous using the successor > > > operation. > > > > Through what successor operation do you get the ordinal omega? .... > Please identify something you see as incorrect or don't understand. Read above. Cardinals are not *all* obtained from the previous using the powerset operation. Ordinals are not *all* obtained using the successor operation. Hence my questions. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Lester Zick on 26 Oct 2006 19:22
On 26 Oct 2006 14:04:11 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >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: At least we can agree on this. >> 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 ~v~~ |