An uncountable countable set
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From: Virgil on 28 Oct 2006 17:39 In article <4543a5f0(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > imaginatorium(a)despammed.com wrote: > >> Anyway, I'm getting a giggle from hearing about you "reading" Robinson; > >> makes me wonder if that's how you can find anything of merit in > >> Lester's endless drivel - you just cruise through looking for an > >> attractive sentence here or there? > > > > If you don't realize that the words are supposed to convey rigorous > > mathematics, you can read a math book the same way that you do a novel. > > I fear that most undergraduates who are not math majors read their math > > books this way. > > > > Those poor, lowly undergraduates.... The math majors among them are still way better off than TO, at least as regards reading and understanding rigorous mathematics
From: David Marcus on 28 Oct 2006 17:44 Virgil wrote: > In article <45439743(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > > The purpose being to try to obscure details of the stated problem. > > That does seem to be TO's purpose. > > The stated problem was [ with one modification]: > Given an initially empty vase. > Given the infinite set of finite natural numbers, staring with 1, and a > ball with each number marked on it. > At times in minutes before noon: > at t = 1/n balls numbered 10*(n -1) +1 to 10*n are inserted into the > vase and then in that same instant ball n is removed. > [At noon, a cube is placed in the vase.] > What is the state of the vase at noon ? Seems to me that the cube won't fit in the vase because the vase is full of balls that have infinite non-standard reals marked on them. -- David Marcus
From: Virgil on 28 Oct 2006 18:21 In article <4543ad83(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > imaginatorium(a)despammed.com wrote: > > Tony Orlow wrote: > >> imaginatorium(a)despammed.com wrote: > > > > <snip> > > > >>> Here's another question - I' ve asked before, so I don't hold out much > >>> hope of an answer, but anyway: Suppose you could ask Abraham Robinson > >>> what he thought of your ideas: what do you suppose he would say? Do you > >>> think he might just latch onto the IFR, N^L=S (whaddeveritwas), your > >>> T'rrible numbers, the twilight zone, etc., or do you suppose he would > >>> dismiss it as total nonsense? > >> I suppose that depends on whether he liked me. I don't think hed find my > >> ideas objectionable. He was obviously an original thinker. > > > > What do you mean by "objectionable"? > > That he would object to any of my conclusions, or even my logic. Robinson would object to both. One must be able to criticize one's own thoughts quite carefully, and eliminate any illogic from them to develop what Robinson did. Which would make Robinson equally able to criticize other's illogic. Of which TO has a lion's share. > > How can whether you like someone > > affect whether you think they are making mathematical sense or not? > > Emotions and intuition play a big role in "rational" decisions, whether > you like it or not. Not in rational decisions about the validity of mathematical arguments. > > As > > you say, Abraham Robinson was an original thinker, but I don't think I > > would be insulting him to say no more original in particular than > > thousands of other mathematicians all brighter than me. > > > Do you think you are an "original thinker"? > > Do you? It seems like almost everything that comes out of my mouth (via > my fingers and this computer) is objectionable to someone here, and yet, > it all fits together. Only in TO's mind. > I get the feeling Robinson would tire of my lack > of rigor Agreed > but probably agree with most of my conclusions TO's conclusions directly violate Robinson's logic.
From: Virgil on 28 Oct 2006 18:21 In article <4543a3fa(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > I mean the formula relating the number In to the number OUT for any n. > That is given by out(in) = in/10. Until TO can show that his "formulaic relationships" must produce a proper partial order on sets similar (in being a proper well ordering) to the proper well ordering defined by cardinality, any reference to "formulaic relationship" is entirely speculative and irrelevant to the relative sizes of sets.
From: cbrown on 28 Oct 2006 19:09
Tony Orlow wrote: <snip> > > t=-1/n ^ t=0 -> -1/n=0. T v F? T. However, in a mathematical argument it is equally true that (assuming t is a real and n a natural): t=-1/n ^ t=0 -> -1/n > 7 Cheers - Chas |