An uncountable countable set
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From: Lester Zick on 2 Nov 2006 13:34 On 2 Nov 2006 07:58:34 -0800, "Randy Poe" <poespam-trap(a)yahoo.com> wrote: > >Lester Zick wrote: >> On 31 Oct 2006 11:54:23 -0800, "Randy Poe" <poespam-trap(a)yahoo.com> >> wrote: >> >> > >> >Lester Zick wrote: >> >> On 30 Oct 2006 19:47:06 -0800, "Randy Poe" <poespam-trap(a)yahoo.com> >> >> wrote: >> >> >> >> > >> >> >Lester Zick wrote: >> >> >> On 30 Oct 2006 10:46:23 -0800, "Randy Poe" <poespam-trap(a)yahoo.com> >> >> >> wrote: >> >> >Why, do you think that there's a least integer? What, >> >> >around -1000? >> >> >> >> If 1 is an integer then 1 would be least would it not? >> > >> >No, 0 is an integer with the property 0 < 1. >> >> Thanks for the heads up. What makes you think it's true? > >If you don't accept 0 < 1, we really aren't talking >about the same mathematics at all. And which mathematics are you talking about, Randy? True math? Or false math? Or set theory? >> >> >Proof: >> >> >A least member x0 would have the property that >> >> >x0 <= x for all other members x. >> >> > >> >> >Let x0 be any integer. x0-1 is also an integer, which is <x0. >> >> >Thus x0 can't be a least member. >> >> > >> >> >Similar argument for x0 being any real. >> >> >> >> Not if the integers under discussion are positive: >> > >> >When we say "the least member of the set of integers" they >> >are not all positive, since the set of integers is not all positive. >> >> If you say so. > >It's whoever says so. The phrase "the set of integers" >includes everything that is an integer, whoever utters >that phrase. So who is supposed to care when you also don't claim any of this is true? >> >When we say "the least member of the set of POSITIVE >> >integers", they are all positive. >> >> No lie? > >Yes, the phrase "the set of positive integers" refers >to everything which is not only an integer, but is >also positive. Gee that's just swell. But the more pressing problem I see is whether it's true. >> >> is 1 an integer? Is it positive or negative? >> > >> >It is a positive integer. >> > >> >But it isn't the smallest member of the set of integers. >> >> It's also not imaginary. > >Uh, right. Was that supposed to be relevant? Is "negative" supposed to be relevant? >> >> It certainly isn't negative unless so stated. >> >> Ergo it is not negative nor are integers negative unless explicitly >> >> qualified. You make one propositional logic error then try to sneak in >> >> an implicit qualification to justify your original error. >> > >> >Eh? How is it an "implicit qualification" to mean "the set >> >of integers" when the set specified is "the set of integers"? >> >> I don't recall as the original said anything about sets. >> >> >Wouldn't be adding the word "positive" when it is left out >> >be considered adding a qualification that wasn't present? >> >> Beats me. > >OK, then I'll help you out. If somebody says "the set >of integers" and you interpret this to mean "everything >which is an integer and which is also positive" then >you have added "which is also positive" to the >original qualifications. So? If you strike common predicates you're still left with "integers" on the one hand and "no . . . reals" on the other and my original question and observations are both relevant and appropriate. >> >How exactly does the "set of integers" have "implicit >> >qualifications" that "the set of positive integers" doesn't? >> >What additional restriction is added to Z+ to make it Z? >> >> Ask somebody who cares. > >Ah, my mistake. I thought your continued discussion >of this topic meant that you cared, or at least cared >about what you were writing. I care about what you can demonstrate to be true, Randy, and not just whatever pops into your head you learned in modern math class today. ~v~~
From: MoeBlee on 2 Nov 2006 14:02 Lester Zick wrote: > On 1 Nov 2006 14:59:05 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > >> >That there are different kinds of numbers does not entail that set > >> >theory cannot be a foundation. > >> > >> Nor does it entail that set theory can be. > > > >True. But so what? I don't know of anyone who claims that the mere fact > >that there are different kinds of numbers is what enables set theory to > >be a foundation. > > So why are you arguing about it then? Set "theory" is not a theory at > all. It's just a group of set analytical techniques having nothing to > recommend it but the fact that x many people use it and call it home. > You don't even try to claim it's true. So whatever you think you have > to recommend it as some kind of foundation is largely irrelevant. Thanks, but no thanks for the uninformed rant. MoeBlee
From: MoeBlee on 2 Nov 2006 14:21 Lester Zick wrote: > On 1 Nov 2006 16:57:47 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > >> On 31 Oct 2006 15:22:10 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> > >> >Lester Zick wrote: > >> >> On 30 Oct 2006 17:45:48 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> >> > >> >> >Lester Zick wrote: > >> >> >> According to MoeBlee mathematical definitions require a "domain of > >> >> >> discourse" variable such as IN(x) and OUT(x). > >> >> > > >> >> >I did not say that. Regarding a particular definition I gave, I > >> >> >explained to you that the variable ranges over the domain of discourse > >> >> >of any given model. I didn't say, in general, that definitions > >> >> >"require" variables (some defininitonal forms do require variables, but > >> >> >not all definitions do), nor did I suggest using variables in the > >> >> >mindless way you have done in certain examples you've posted that > >> >> >misrepresent the actual definition I gave. > >> >> > >> >> Then exactly why did you go apeshit over the issue, Moe? > >> > > >> >Because you kept representing that I said what I did not say, you > >> >idiot. > >> > >> And you know that how, Moe? Because the material you deleted backs you > >> up? Or because the material you deleted doesn't back you up? > > > >Deleted material? I haven't deleted any posts. > > Uh oh, Moe, this borders on deliberate misrepresentation since I refer > specifically to "material you deleted" and you try to evade the issue > by claiming you haven't "deleted any posts". No, since in the VERY NEXT SENTENCE I addressed not deletion of posts but redacting of them. So when you said 'deleted material', I addressed both possible senses of that. I didn't say that you had claimed the first sense, but rather I simply addressed both senses, since 'deleted material' is ambiguous as to which sense. > I'm not even sure how you > might go about deleting any posts to begin with. But you sure have > deleted a lot of material in replies to my posts then demanded I go > and research the significance of deleted material to satisfy your > claims. I think it's becoming pretty obvious here who's being evasive. I made no such demand. And I've evaded nothing. > > > And the fact that I > >haven't included every previous quote in every of my posts is not an > >issue unless you show some lack of inclusion that did materially > >distort what you said. > > Unless I show??? It's your claim, sport, not mine. No, it's YOUR claim that my not including all quoted material is some kind of issue. It's not an issue unless the lack of complete inclusion is materially distorting. > You need to start > supporting your own claims for a change and stop demanding others do > it for you. You need to stop claiming that I demand anyone support my own claims. > > > I'm not going to commit to including all > >accumulated previous quoted posts in each of my replies. And I may trim > >to certain quotes and portions of previous posts to emphasize the scope > >of my particular interest in what I am replying to. If you claim a > >material distortion, then go ahead and show what you think has been > >distorted, if you like. > > You're the one who claims a material distortion, slick. You're completely mixed up, as usual. You distorted my formula and points I made. I already demonstrated that many posts ago. THEN YOU claimed that my not including all quoted material is at issue. But that is not at issue unless my not including all quoted material causes material distortion. So, no, *I* don't claim that my not including all quoted material causes material distortion. Quite the contrary. > >Meanwhile, what backs me up are the posts in the threads, including > >your own posts in which you mangled my formulas and what I had said, > >which (as far as I know) are not deleted by you and remain just as they > >were posted. > > Then you can actually prove your claims for a change? > > >Now, since you're whining about wanting to move on, then do it. Or > >don't and continue to whine about it. But no matter what you do, you > >always manage to make yourself into an utter fool and boor doing it > >anyway. > > I wasn't the one whining about wanting to move on, Moe(x), you were. YOU, not I, were the one to say "maybe we can move on" (or whatever exact quote you made). > I'm perfectly content to stay right here while I refine my definitions > and terminology to bring them into better conformance with standard > mathematical usage and more appropriate neomathematical forensic > modalities. MoeBlee
From: cbrown on 2 Nov 2006 15:44 cbrown(a)cbrownsystems.com wrote: > imaginatorium(a)despammed.com wrote: <snippity snip> > > But consider > > a Feynmann space-time diagram (you know, the thing where an electron > > colliding with an antielectron, preceded by that antielectron having > > been spontaneously generated together with a(nother?) electron, can be > > viewed as a single electron travelling through a path so zigzag it goes > > backwards in time * details need correction). Suppose something > > "happens" to the thing going backwards in time: does this require > > function g() this time? Your interpretation seems to imply that if for > > example a ball is put in a vase from two o'clock to half past four, the > > corresponding interval for its presence is [2, 4.5). I don't see any > > reasonable basis for this claim. > > > > Bah. Your argument that "a precedes b therefore (whatever)" ignores the > fact that a /must/ precede b. Or words to that effect. Sorry - I was channeling TO a bit too strongly here; and your comments deserve a bit more serious answer. The original problem statement /only/ speaks of ball additions and removals (causes); it is up to us to deduce (from simple assumptions) whether a ball is actually /in/ the vase (effect) at any time at all. The difficulty here is that we speak of several things "happening" simultaneously; and yet (by Tony's claim that if something happens /at/ time t, something caused it to happen /at/ time t), there is some sort of ordering imposed on these simultaneous "happenings": if the thing that happens is a "cause", it takes precedence in this ordering over something which is an "effect". So if a ball is added /at/ time t, the ball is then in the vase /at/ time t; this is consistent with "something happened /at/ time t (the sudden appearance of a ball); so something "first" caused it (the adding of a ball) /at/ time t". The ball is added "at the beginning of" time t; and /next/ we look to see that there is, indeed, a ball in the vase at time t. Similarly, if a ball is removed at time t, then the ball is not in the vase at time t. (Side bar: I've always been slightly tweaked by the events at time t = -1. Ball 1 is simultaneously added to and removed from the vase. Is Ball 1 ever actually "in" the vase? What if we had said "at time t = 1/n, remove ball n and add balls (10*(n-1)+1) to 10*n inclusive?" Would we actually know that Ball 1 isn't /still/ in the vase? In which case, we've been wrong all along - the vase is /not/ empty at noon: Ball 1 is in the vase at noon!). As regards the Feynmann diagram: Well, we lose a bit due to a lack of an assumption of time symmetry; but I would say that we could "fix" this by claiming that if time is "going in reverse", then the implicit precedence of "causes" and "effect" is reversed: If a ball is in the vase at t = 0, and not in the vase for t<0, then the ball was "anti-added" at time 0; i.e., "first" the ball is in the vase "for the last time"; "next", the ball is anti-added at the "end" (in reverse-time) of time 0. Similarly, if the ball is not in the vase "for the last time" at time t, then we deduce that the ball is "anti-removed" at time t. Hmmmm... it's a bit of a stretch I admit. As regards "The ball is in the vase from t1 to t2": This is always a /deduction/ from the original problem, which makes no definitive statements about balls being "in" the vase at all; so I would claim that "the ball is in the vase from 2 to 4" only makes sense as a deduction from "the ball is added at 2, and removed at 4", which yields (according to the rules above) the ball being in the vase during the half-open interval interval [2,4). All this being said, I don't think the assumption "If something happens /at/ t, something must cause it /at/ t" is particularly useful or even sensible. Even better would be to realize that in problems of this sort, we only require: "If something happens at time t, it must be logically deducible from the facts given in the problem". The only "causes" here are the initial assumptions of the problem; and the only "effects" are logical deductions from these "causes". What "causes" ball 2 to be in the vase at time -2/3? The only sensible answer I can give is that it is an "effect" that follows from our definitions of what it means for a ball to be in the vase at all (thus my premises (1)..(4)), combined with (5), (6), and (7). These "causes" don't "happen" at "some time t"; they are ever present. Likewise, the only sensible answer to "what causes the vase to become empty at noon, when nothing actually happens at noon?" is "as with all other effects, it logically follows from the problem statement and our assumptions". Cheers - Chas
From: cbrown on 2 Nov 2006 15:45
David Marcus wrote: > cbrown(a)cbrownsystems.com wrote: > > imaginatorium(a)despammed.com wrote: > > > > You say f() correctly captures the "removal > > > _at_ time 0", because f(0) is the value after the change. > > > > Right - because the event which we call "the vase becomes empty at 0" > > must be "preceded" by some event which /causes/ that "becoming" > > (regardless of rest frame). In this case, BTW, "a precedes b" means > > "the time at which a occurs <= the time at which b occurs, for evey > > rest frame". Although giving that away is really a form of cheating. > > > > Under these "obvious" constraints, f() describes a certain real world > > situation; if the 'cause' of f(0) = 0 is that the indicator function > > k(t) = 1 iff a ball is removed at time t=0 has k(0)=1 . The same, sadly > > or happily, cannot be said of h(). > > What's with the empty parentheses? The names of the functions are "f" > and "h", not "f()" and "h()". > Hey! Don't blame me! He started it! Cheers - Chas |