An uncountable countable set
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From: Virgil on 20 Oct 2006 15:55 In article <4539125e$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> Your examples of the circle and rectangle are good. Neither has a height > >> outside of its x range. The height of the circle is 0 at x=-1 and x=1, > >> because the circle actually exists there. To ask about its height at x=9 > >> is like asking how the air quality was on the 85th floor of the World > >> Trade Center yesterday. Similarly, it makes little sense to ask what > >> happens at noon. There is no vase at noon. > > > > Do you really mean to say that there is no vase at noon or do you mean > > to say that the vase is not empty at noon? > > > > If noon exists at all, the vase is not empty. All finite naturals will > have been removed, but an infinite number of infinitely-numbered balls > will remain. Which balls do not exist outside of TO's overly fertile imagination. And certainly do not exist in the original GE.
From: Virgil on 20 Oct 2006 15:56 In article <453912c1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> David Marcus wrote: > >>> Tony Orlow wrote: > >>>> Virgil wrote: > >>>>> In article <4533d315(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>>>> Then let us put all the balls in at once before the first is removed > >>>>>>> and > >>>>>>> then remove them according to the original time schedule. > >>>>>> Great! You changed the problem and got a different conclusion. How > >>>>>> very....like you. > >>>>> Does TO claim that putting balls in earlier but taking them out as in > >>>>> the original will result in fewer balls at the end? > >>>> If the two are separate events, sure. > >>> Not sure what you mean by "separate events". Suppose we put all the > >>> balls in at one minute before noon and take them out according to the > >>> original schedule. How many balls are in the vase at noon? > >>> > >> empty. > > > > Suppose we put ball n in at 1/n before noon and remove it at 1/(n+1) > > before noon. How many balls in the vase at noon? > > > > At all times >=-1 there will be 1 ball in the vase. Which ball will that be at noon, TO?
From: Virgil on 20 Oct 2006 16:00 In article <453912ec(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> David Marcus wrote: > >>> Tony Orlow wrote: > >>>> Virgil wrote: > >>>>> In article <4533d315(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>>>> Then let us put all the balls in at once before the first is removed > >>>>>>> and > >>>>>>> then remove them according to the original time schedule. > >>>>>> Great! You changed the problem and got a different conclusion. How > >>>>>> very....like you. > >>>>> Does TO claim that putting balls in earlier but taking them out as in > >>>>> the original will result in fewer balls at the end? > >>>> If the two are separate events, sure. > >>> Not sure what you mean by "separate events". Suppose we put all the > >>> balls in at one minute before noon and take them out according to the > >>> original schedule. How many balls are in the vase at noon? > >> empty. > > > > Why? > > > > Because of the infinite rate of removal without insertions at noon. Except that no balls are removed "at noon", so the rate of removal "at noon" is zero. What TO is trying to say is that the set of rates of removal near noon (in any neighborhood of noon) are unbounded.
From: Lester Zick on 20 Oct 2006 16:23 On Fri, 20 Oct 2006 09:17:25 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >MoeBlee wrote: > >> Han de Bruijn wrote: >> >>>The confusion stems from the fact that I cannot and shall not understand >>>the _infinite_ counterparts of the finite cardinals and ordinals. >> >> How can you understand if you won't read a book that explains it? (By >> the way, Halmos is a good book, but it's just an overview; it doesn't >> give you the full explanations that you need.) >> >> So you seem to think it is better to spout nonsense on the Internet >> about a subject you cannot possibly understand since you insist that >> you won't. > >How can you say this? I understand very well that infinite cardinals and >ordinals simply do not exist. Han, I have to disagree here. There certainly are infinite cardinals and a corresponding number of infinite ordinals. The difficulty is that there is no open set of such things. They're all defined within boundaries of infinitesimals. ~v~~
From: Lester Zick on 20 Oct 2006 16:24
On Fri, 20 Oct 2006 01:40:33 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <9806$45387805$82a1e228$25512(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >> MoeBlee wrote: >> >> > Han de Bruijn wrote: >> > >> >>The confusion stems from the fact that I cannot and shall not understand >> >>the _infinite_ counterparts of the finite cardinals and ordinals. >> > >> > How can you understand if you won't read a book that explains it? (By >> > the way, Halmos is a good book, but it's just an overview; it doesn't >> > give you the full explanations that you need.) >> > >> > So you seem to think it is better to spout nonsense on the Internet >> > about a subject you cannot possibly understand since you insist that >> > you won't. >> >> How can you say this? > >One word at a time. > >> I understand very well that infinite cardinals and ordinals simply do >> not exist. > >And we understand that, while they have no more physical existence than >any other mathematical ideas, they do have just as much mathematical >existence as any other mathematical ideas. Just out of curiosity, Virgil, what exactly is a mathematical idea? ~v~~ |