Cantor Confusion
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From: Virgil on 19 Oct 2006 14:18 In article <cab6b$45373361$82a1e228$6838(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > David Marcus wrote: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > >>MoeBlee schrieb: > >> > >>>First you say the notion of 'rational relation' (whatever that means) > >>>"cannot be expressed by mathematical notion". Then you challenge me to > >>>say what part of your proof is in conflict with set theory. What is the > >>>notion of 'rational relation' that "cannot be expressed by mathematical > >>>notion"? Are defining a certain relation in set theory or are you > >>>definining a relation you claim not to exist in set theory? > >> > >>Meanwhile there are many who understand the binary tree. Perhaps you > >>will follow the discussion, then you may understand it too. > > > > But, no one seems to understand your binary tree. Please state your > > claim and its proof using standard terminology and words that you > > clearly define. For example, use the terminology that Halmos uses in > > "Naive Set Theory". If you don't like that book, then pick a book you > > like and tell us what it is. > > There are many readers here who DO understand Mueckenheim's binary tree. > And no, binary trees will not be found in Halmos' "Naive Set Theory". > Because it's too naive, I suppose .. > > Han de Bruijn If you are one of those who claims to understand "Mueckenh"'s trees, pehaps you can explain his alleged bijection between edges and paths in a binary tree which has no leaf nodes.
From: Virgil on 19 Oct 2006 14:19 In article <3f49a$453733d3$82a1e228$6838(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > David Marcus wrote: > > > Bohmian Mechanics is a deterministic theory that avoids the measurement > > problem, satisfies Bell's Inequality (as do all theories of quantum > > mechanics), agrees with all experiments, and doesn't produce negative > > probabilities. So, it seems to be a better theory than the one you > > constructed. > > Sure. Let's go back to the dark ages of Newtonian Mechanics. > > Han de Bruijn As HdB is already in the mathematical dark ages, it will be a short trip for him.
From: Virgil on 19 Oct 2006 14:22 In article <1161250680.844152.208670(a)m7g2000cwm.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <1161182168.538010.12650(a)f16g2000cwb.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > > N = omega = aleph 0. How should one of them have different character? > > > According to Cantor, set theory deals with actual infinity, not with > > > potential. > > > > Cantor died in 1918. Things have progressed a bit since then. > > Not the knowledge about infinity. On the contrary, it has been > forgotten and has been applied carelessly and false. While there are some, like "Mueckenh", who have not progressed beyond 1918, and have even regressed, not everyone is so backward.
From: Virgil on 19 Oct 2006 14:51 In article <1161275085.297528.78850(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > There are only a limited number of messages that it is > > possible to communicate. One of these messages describes a > > larger number than any of the other messages (description includes > > description of any compression method used). > > Correct. There will be a largest number ever communicated. But that > does not mean that this number is fixed as yet (unless you would favour > strict determinism.) That "number" is not actually a number but is a function of time. ...... > > Yes, but it is impossible to have such an infinite set of numbers with > finite differences. It is only impossible for those who believe it to be impossible. > > > > >You assume that only the one is changed, the other is not. > > > But you seem not to be aware that in natural numbers size and > > > cardinality are strictly the same > > > > I take it you mean that for a set of natural numbers of the form > > {1,2,3,...,n}, the cardinality is equal to the size of the maximum > > element. > > This is only true if the set has a maximum element > > It is true for a set of finite numbers. It is true for finite sets but not necessarily for sets of finite numbers. Bounded open intervals are bounded sets of finite numbers but do not contain any maximum or minimum elements. > An infinite number of finite > numbers would imply an infinite difference but that would imply an > infinite number. (Given actual infinity.) That sounds remarkably like one of TO's delusions. Since the set of real numbers contains an isomorphic image of the naturals, "Mueckenh" is claiming that there must be infinite real numbers. > What is Piffle? A descriptive word, describing the tangled though processes of a "Mueckenh". > > I wonder how beauty would look like without physics. Totally unaffected. The absence of quantum theory or relativity would not affect the beauty of the Venus de Milo a whit.
From: Virgil on 19 Oct 2006 14:58
In article <1161275307.667857.67400(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <1161159181.827351.41670(a)e3g2000cwe.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > > Wrong. The connection between finite paths and partial sums of edges > > > > > leads to > > > > > (1-(1/2)^n+1)/(1 - 1/2) edges per path. > > > > > Which, as written, is negative for all positive naturals n. > > > > Indeed? In your world? Then I can guess why your vase > > > sometimes empty. > > > And (1-(1/2)^n+1)/(1 - 1/2) <= 4 for all n in N, > > > and lim_{n -->oo} (1-(1/2)^n+1)/(1 - 1/2) = 4. > > I knew this calculation when seeing your reply. But I have not yet > understood why you consider 4 as being negative. My error. I misread a sign. > > > > And if edges are to be split, so can paths be split, and into as many > > pieces. > > Please split the paths. Then you will get more pieces. You will get a > larger set which consists of what? Any splitting of paths leaves as many infinite paths as one started with plus the finite front bits (from root node to some other node) cut off of them, but the finite front bits are not all different, as two different infinite paths can have an arbitrarily large finite sized front bit in common. In fact every front bit is the front bit of uncountably many paths. |