An uncountable countable set
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From: Virgil on 23 Oct 2006 14:29 In article <453cacc8(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <453bc7c9(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <453b326d(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>> Virgil wrote: > >>>>> In article <4539000e(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>> Claimed but not justified. TO's usual technique! > >>>> You didn't justify yours. It's clearly nonsensical. It pretends there's > >>>> a time between noon and all times before noon. > >>> I only claim there is a time between any time before noon and noon. > >>> > >> When does the vase become empty? > > > > It is empty at noon and is not empty at any time before noon, but I have > > no idea what TO means by "When does the vase become empty?", as it seems > > to imply a continuity at 0 that does not exist. > > > > You claim that time is crucial to this problem, but you claim that time > is discontinuous? Quite the contrary, time IS continuous, and I have never claimed otherwise. But functions of time need not be, and in the number of balls function cannot be. > Define "time". Time is a real variable. > Everything that occurs in time includes > at least one moment. Name one moment when the vase is emptying. The lack of any such moment is one reason that the "number of balls" as a function of time cannot be continuous at noon. Another is that noon is a cluster point of other discontinuities of that function.
From: MoeBlee on 23 Oct 2006 14:34 Lester Zick wrote: > You and he just have different perspectives on the problem and nothing > in what you have to say has any relevance to what Tony believes any > more than what Tony believes has any relevance to what you believe. Differing perspectives are welcome. But that is different from simply saying incorrect things about the technical points and also from giving the kind of woozy arguments he gives for his non-axiomatic mathematics. MoeBlee
From: Tony Orlow on 23 Oct 2006 14:39 David Marcus wrote: > Tony Orlow wrote: >> David Marcus wrote: >>> Tony Orlow wrote: >>>> cbrown(a)cbrownsystems.com wrote: >>>>> (5) If a ball is placed in the vase at some time t, it must be in >>>>> accordance with the description given in the problem: it must be a ball >>>>> with a natural number n on it, and the time t at which it is placed in >>>>> the vase must be -1/floor(n/10). >>>>> >>>>> <snip> >>>> Those all look reasonable to me as I read them. I don't see any >>>> statement regarding the fact that ten balls are added for every one >>>> removed, though that can be surmised from the insertion and removal >>>> schedule. That's the salient fact here. You never remove as many as you >>>> add, so you can't end up empty. >>> What about #5? It says that every ball in the vase has a natural number >>> on it. Do you agree with that? >> That is in the problem statement. Therefore, nothing transpires at noon, >> since -1/n<0 for all n e N. > > If I read this correctly, you agree that at all times every ball that is > in the vase has a natural number on it, but at noon you say that there > is a ball in the vase that does not have a natural number on it. Is that > correct? No. I am saying that if only finite iterations of the ball process occur, then noon never occurs in the experiment to begin with. If noon DOES exist in the experiment, then that can only mean that some ball n exists such that 1/n=0, which would have to be greater than any finite n. > >>>> Either something happens an noon, or it doesn't. Where do you stand on >>>> the matter? >>> What does "something happens" mean, please? I really don't know what you >>> mean. >> ??? Do you live in the universe, or in a static picture? When "something >> happens" o an object, some property or condition of it "changes". That >> occurs within some time period, which includes at least one moment. >> There is no moment in this problem where the vase is emptying, >> therefore, that never "occurs". If you are going to insist that time is >> a crucial element of this problem, then you should at least be familiar >> with the fact that it's a continuum, and that events occurs within >> intervals of that continuum. > > Thanks. That explains what "something happens" means. Now, please > explain what "emptying" means. > "Empty" means not having balls. To become empty means there is a change of state in the vase ("something happens" to the vase), from having balls to not having balls. Now, when does this moment, or interval, occur?
From: MoeBlee on 23 Oct 2006 14:40 Tony Orlow wrote: > In Chapter III, section 3.1.1, he states: > > "There is no smallest infinite number. For if a is infinite then a<>0, > hence a=b+1 (the corresponding fact being true in N). But b cannot be > finite, for then a would be finite. Hence, there exists an infinite > numbers [sic] which is smaller than a." I'll try to take a look at the book soon, but I very strongly suspect that he's using 'infinite' not to refer to cardinality, but rather to position in certain orderings. That is fine, as long as we understand the terminology in the context. As far as I know, it doesn't contradict that there is a least infinite cardinality. MoeBlee
From: MoeBlee on 23 Oct 2006 14:44
MoeBlee wrote: > I deny > that there are other senses of the word; I'm just telling you exactly > what I mean in this context. Of course I meant I do NOT deny that there are other senses. MoeBlee |