The Definition of Points
in [Math]
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From: Virgil on 31 Mar 2007 22:44 In article <460f19f5(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460ef650(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Bob Kolker wrote: > >>> Tony Orlow wrote:>> > >>>> Measure makes physics possible. > >>> On compact sets which must have infinite cardinality. > >>> > >>> The measure of a dense countable set is zero. > >>> > >>> Bob Kolker > >> Yes, some finite multiple of an infinitesimal. > > > > In any consistent system in which there are infinitesimals, none of > > those infinitesimals are zero. > > On the finite scale, any countable number of infinitesimals has zero > measure. Again with the undefined terms. What does it mean to have zero measure in a field having infinitesimals?
From: Virgil on 31 Mar 2007 22:44 In article <460f1a41(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460ef372$1(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <460e82b1(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>> > >>>> As I said to Brian, it's provably the size of the set of finite natural > >>>> numbers greater than or equal to 1. No, there is no last finite natural, > >>>> and no, there is no "size" for N. Aleph_0 is a phantom. > >>> All numbers are equally phantasmal in the physical world and equally > >>> real in the mental world. > >> Virgule, you don't really believe that, do you? You're way too smart for > >> that... :) > > > > While I have seen numerals in the physical world, I have never seen any > > of the numbers of which they are only representatives. > > > > And I suspect that any who claim to have done so have chemically > > augmented their vision. > > Is that wrong? haha. Anyway... > > You have seen two apples, and three? > Are apples numbers?
From: Virgil on 31 Mar 2007 22:46 In article <460f1b3e(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460ef839(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <460ee056(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > > > >>>> Please do expliculate what the contradiction is in an uncountable > >>>> sequence. What is true and false as a result of that concept? > >>> A mathematical sequence is a function with the naturals as domain. > >>> If TO wishes to refer to something which is not such a function, he > >>> should not refer to it as a sequence if he wishes to be understood in > >>> sci.math. > >>> > >>> > >> Pray tell, what term shall I use???? > > > > TO is so inventive in so many useless ways that I cannot believe that > > his imagination will fail him in such a trivially useful way. > >>>>> I know you are incapable of actually thinking about all the elements of > >>>>> N, > >>>>> but that is your problem. In any case, N is not an element of N. > >>>>> Citing Ross as support is practically an admission that you are wrong. > >>>>> > >>>>> Stephen > >>>>> > >>>> Sure, of course, agreeing with someone who disagrees with you makes me > >>>> wrong. I'll keep that in mind. Thanks.. > >>> > >>> It is not so much that Ross disagrees with one person, it is that he > >>> disagrees with everyone, frequently including himself. > >> Ross has a vision, even if not axiomatically expressed. In fact, he's > >> entirely honest about that, expounding an axiom free system. I like > >> Ross. So do you. Admit it. :) > >> > > > > > > Like Russell? > > > > What is there about him to like? > > You don't like Russell? I don't know him well enough to like or dislike. I dislike his anti-mathematical idiocies.
From: Tony Orlow on 31 Mar 2007 22:52 Virgil wrote: > In article <460f00a0(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Look back. The nth is equal to n. Inductive proof holds for equality in >> the infinite case > > Not in vN. I know that statement is not generally acceptable. I don't care. It's true. Infinite-case induction has not been disproved, despite Chas' very excellent effort, and some other that was lame. In other words, it's not contradictory. And inductive proofs do not work that way. One can prove by > induction that something is true for each natural, but that does not > create any infinite naturals for which it is true. You can agree with your buddies these are the rules of your club, and you can hang around the pickup drinking cans of beer and talking about trucks and ladies, but somes of us gots interstates to travel, and, you know, big cities to deliver to. Where an equality is proven true for all x>k, then any positive infinite value is greater than any finite k, and the proof holds. Simple clear logic. Refute, please.
From: Tony Orlow on 31 Mar 2007 22:54
Virgil wrote: > In article <460f0317(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > >> There are not zero, nor any finite number of reals in (0,1]. > > There are every finite and more of reals in (0,1]. You mean any sequential ordering of the reals in (0,1] will contain elements in finite positions, plus more. Same thang. Tru dat, yo. Tony |