An uncountable countable set
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From: Tony Orlow on 27 Oct 2006 20:36 Virgil wrote: > In article <45421a34(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> David Marcus wrote: > >>> So, "noon exists" in this case, even though nothing happens at noon. >> Not really > > Yes really. Nope. (see? I can be an imbecile too)
From: Virgil on 27 Oct 2006 20:36 In article <4542a36d(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > cbrown(a)cbrownsystems.com wrote: > Specify the largest natural, and I'll grant you that. TO on his "largest natural" kick again. When TO can produce 4 sided triangles on request, or points of intersection of parallel lines in Euclidean spaces, only then will he have the right to ask for largest naturals. > > The "occurence" of these events (ball insertions and removals at > > particular times) is described by (1), (5), (6), and (7). > > There is the event of becoming empty, i.e., in(t)-out(t)=0. Oh, except, > that never happens. Except that if it doesn't happen nothing else can happen either, since without noon, there is no forenoon. > > > > There is no "becoming" empty described in (1)..(8). There is only > > "being" empty; which is described by (1), (2), (3), and (4), and (8). > > > > Formulate it, and behold your error. We formulated it and beheld a lot of TO's errors but none of our own. The only relevant question is "According to the rules set up in the gedankenexperiment, is each ball which is inserted into the initially empty vase before noon also removed from the vase before noon?" An affirmative answer guarantees that the vase is empty at noon. A negative answer directly violates the conditions of the problem. So, of course, TO answers negatively.
From: Tony Orlow on 27 Oct 2006 20:39 Virgil wrote: > In article <45421ba8(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> On the surface, you math appears correct, but that doesn't mend the >> obvious contradiction in having an event occur in a time continuum >> without occupying at least one moment. It doesn't explain how a >> divergent sum converges to 0. Basically, what you prove, if V(0)=0, is >> that all finite naturals are removed by noon. I never disagreed with >> that. However, to actually reach noon requires infinite naturals. > > Where do these alleged infinite naturals come from? Then are certainly > not available in the original gedankenexperiment, which takes place in a > mathematical world compatible with ZF or NBG. They come from t=-1/n and t=0, thus 0=-1/n. Idiot. > > They spring full-blown from TO's "intuition", which is hostile to all > standard mathematics, and so irrelevant to all standard mathematics. > > And the gedankenexperiment occurs in standard mathematics. t=-1/n ^ t=0 -> -1/n=0. T v F?
From: Virgil on 27 Oct 2006 20:41 In article <MPG.1fac6c84dc2a222989793(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Tony Orlow wrote: > > David Marcus wrote: > > > Now, V is the > > > sum of the B_n. As t approaches zero from the left, V(t) grows without > > > bound. In fact, given any large number M, there is an e < 0 such that > > > for e < t < 0, V(t) > M. We also have that V(0) = 0 (as you agreed). > > > > > > Now the question: How do you explain the fact that V(t) goes from being > > > very large for t a little less than zero to being zero when t equals > > > zero even though none of the B_n are changing near zero? > > > > I'll consider answering that when you correct the errors above. Sorry. AS there are no errors in David's analysis, but many in TO's, that indicates that TO has no reasonable answers. But that is hardly news.
From: Virgil on 27 Oct 2006 20:42
In article <4542a3a5(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > If TO were to support someone reasonably in touch with mathematical > > reality, I should not have regarded it as a "last straw" situation. > > Like Robinson? Robinson does not need, or want, TO's support. |