On Jun 26, 3:56 pm, Virgil <vir...@ligriv.com> wrote: > In article > <d3322ea2-e67e-4dc5-8e32-ebc40b0dd...@l17g2000vbj.googlegroups.com>, > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 26 Jun., 03:03, FredJeffries <fredjeffr...@gmail.com> wrote: > > > On Jun 25, 2:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 25 Jun., 22:33, FredJeffries <fredjeffr...@gmail.com> wrote: > > > > > > On Jun 25, 12:05 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > Take a circle (it need not be glowing) and as ask the examinee to mark > > > > > > infinitely many intervals by infinitely many endpoints. Shuffle the > > > > > > endpoints such that they slide along the circle in a completely > > > > > > arbitrary way. > > > > > > Completely arbitrary? Not hardly. > > > > > If you wait long enough, it may happen that the endpoints reproduce > > > > just my example of intervals I_n. At least it might happen, it cannot > > > > be excluded (if the configuration is really real). And that's enough. > > > > You're the one who preaches about the rules used to create sequences > > > and > > > sets. In your problem you create the sequence of intervals according > > > to > > > a rule. Yet, in all of your subsequent discussion you completely > > > ignore > > > the rules used to generate the set. > > > And that prevents that you can pinpoint any point where the change > > from countably many intervals to uncountably many intervals could > > occur. By simply continuous sliding of points I defeat your tricks. > > nonsense! > > In the first place, WE neither need nor use any "tricks". We merely use > standard mathematics and standard logic. > > On the other hand, WM DOES use tricks: All sorts of false logic, > incomplete arguments claimed to be complete, and repetition of false > arguments as if repeating them will mak them any les false. > > > > > Can you blame me of non-mathematical action? > > In a mathematical discussion, what need is there for your > non-mathematics and anti-mathmatics? > > > No! If the configuration > > of intervals I_n constructed according to the rules (that I have > > specified), then it can also come into being by a continuous process. > > It has not yet been shown to come into being by any > continuous process, nor has it been shown that, even if it could, that > would make it behave in the impossible ways that WM claims it should.
Note his underhanded use of the term "continuous". I predict that he is going to use that as a way to claim that the cardinality of the number of intervals (or whatever) must be countable also in the limit. He has just enough mathematical knowledge to be a danger to himself and plenty of attitude to be a danger to others.
> > By the way, Archimedes is said to have received some dirty looks from > > his contemporary scholars because he had proved his volume formulas > > for cylinder, sphere and cone by physical bodies and water. They said > > "proved" of course, in Greek of course. I think his method is better > > than ZFC and the like. Truth can only be proved by comparison with > > reality. And as my ring proof clearly shows truth is not with Cantor's > > idea of countability. > > Your alleged "ring proof" may prove something, but does not prove that > your own set of uncovered irrationals in [0, 1] is anything less that > uncountably infinite, nor does it prove, though you keep claiming it, > that every such uncovered irrational is the endpoint of some cluster. > > You have been shown many times how such uncovered irrationals can fail > to be endpoints of any cluster, but have not yet refuted any one of > those demonstrations. > > So one must conclude > that you cannot refute them, and > that they are valid, and > that your counter claims are false. > --