An uncountable countable set
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From: mueckenh on 24 Jun 2006 08:47 Dann Corbit schrieb: > <mueckenh(a)rz.fh-augsburg.de> wrote in message > news:1151079756.995887.177600(a)p79g2000cwp.googlegroups.com... > [snip] > > It is ridiculous to believe in Copernicus in the frame work of the > > bible. Nevertheless I believe in Copernicus. > > What (exactly) is the place in the Bible that contradicts anything said by > Copernicus? There are many places which show that the bible was written by people who knew nothing more than people used to know at 500 BC. Take for instance the creation of the whale among the fishes and its name whale-fish. take the missing hints on Australien animals in Noah's boat. Therefore I do not feel urged to translate German texts to discuss this matter in detail. Here are few of many German texts supporting my obviously correct position (my translations): Salomon (der seine Weisheit von Gott selbst hatte) stellte kategorisch fest: "Die Erde ist ewig in Ruhe, die Sonne geht auf und unter ..." Salomon, who had his wisdom directly from God, stated the earth it at rest in eternity, the sun rises and sets. "Da stand die Sonne und der Mond still, bis sich das Volk an seinen Feinden rächte. Ist dies nicht geschrieben im Buch des Frommen? Also stand die Sonne mitten am Himmel und verzog unterzugehen beinahe einen ganzen Tag". Joshua "Siehe, ich will den Schatten an der Sonnenuhr zehn Striche zurück¬ziehen, über die er gelaufen ist. Und die Sonne lief zehn Striche zurück an der Sonnenuhr, über die sie gelaufen war" (Jesaja). The shadow on the sundial runs back. "Ihren Aufgang vergaß die Sonne" (Habakuk). The sun forgot to rise. And why do you think Galilei was punished by he pope for arguing in favour of Copernicus? Regards, WM
From: mueckenh on 24 Jun 2006 08:49 Dann Corbit schrieb: > "Richard Tobin" <richard(a)cogsci.ed.ac.uk> wrote in message > > > >>>What (exactly) is the place in the Bible that contradicts anything said > >>>by > >>Copernicus? > > > > Joshua 10:13 describes a miraculous event in which Joshua commands the > > sun to stand still, with the result that the day continues until the > > children of Israel had avenged themselves upon their enemies. This, > > it was argued, shows that the cycle of day and night is normally > > caused by the movement of the sun. > > It shows no such thing. The sun moves in the sky (visually). He was just > asking for extended sunshine. But if the shadow on the sundial run back, he would have been flung from the surface of the earth by centrifugal forces. Regards, WM
From: mueckenh on 24 Jun 2006 08:51 Virgil schrieb: > In order to be unambiguous transpositions must be carried out > sequentially, meaning that only countably many can be applied. Not more is required. > > Mueckenh's analysis is not unambiguously a sequence of transpositions. > > Also he does not show that any single transposition can re-order a set > having no first member into one which does have a first member. Of course that is impossible. It is just showing a contradiction in set theory. > > Similarly in the opposite direction, no single transposition will cause > a set with a first element to become one without a first element. Of course that is impossible. It is just showing that there is nothing like an actually infinite set. Regards, WM
From: mueckenh on 24 Jun 2006 08:53 Virgil schrieb: > By definition, a set M is countable if and only if there SOME surjection > g:N --> M exists and is uncountable if no such surjection can exist. > > This means that, given a set M, one must allow ANY function from N to M > to be considered. > > So that given that M(f) exists at all, one is not constrained to only > the function f which defines K(f) and M(f), but can consider whatever > functions imaginable from N to M(f). > > Since it is easy to construct surjections from N to the set of all > finite subset os P(N), it is also easy to do it from N to M(F). Such a function exists from |N --> |R for all real numbers which can be individualized, i.e. which are really real numbers. It was my aim to show this with your arguments. Regards, WM
From: mueckenh on 24 Jun 2006 08:54
Virgil schrieb: > > > What it shows is that the assumption that f is a surjection > > > from N to P(N) leads to a contradiction. If something leads > > > to a contradiction, then it is provably false. > > > > So drop this assumption. There is no mapping, even if surjectivity is > > not at all in question! > > > > Regards, WM > > > Mueckenh is WRONG! > > If surjectivity is not required, all sorts of f's. can exist! > > Consider the following: > f: N --> P(N) : f(n) = {} for all n in N. > Then the image of f is {{}} > Then K(f) = {x in N:x not in f(x)} = N, which shows f is not a > surjection, but can exist if not required to be surjective. > > So there IS a mapping in this case, and Mueckenh is wrong again. So drop this assumption [surjectivity]. There is no mapping [including K as the image of at least one source element], even if surjectivity is not at all in question! Regards, WM |