An uncountable countable set
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From: Virgil on 6 Oct 2006 15:11 In article <1160125052.897509.78620(a)c28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: > > > In article <1160066594.051638.4940(a)i3g2000cwc.googlegroups.com> > > mueckenh(a)rz.fh-augsburg.de writes: > > > Dik T. Winter schrieb: > > > > > By the only meaningful and consistent definition: A n eps |N : > > > > > |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}|. > > > > > Do you challenge its truth? > > > > > > > > No, I never did. But you draw conclusions about it about the set N. > > > > Indeed, > > > > for each finite n, it is true. But this is *not* a proper definition > > > > for > > > > the amounts involved in infinite sets. Given two infinite sets A and > > > > B, > > > > by what method do you determine whether A has more elements than B, or > > > > the other way around? Are there more Gaussian integers than Eisenberg > > > > integers, and if so why? And if not, why not? > > > > > > There are no complete infinite sets. > > > > And I thought you always were talking within the context of the axiom of > > infinity. At least, that is were I am talking. > > I do so, when I contradict your position but I cannot do so when I > explain the correct position. > > Regards, WM The issue of what "position" is correct cannot be established by edict. But that is the only support that "Mueckenh" gives his position.
From: Virgil on 6 Oct 2006 15:19 In article <1160125680.230766.293120(a)i42g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > That is correct according to set theory but it is obviously unserious > because, in a serious theory, the result even of a Gedanken-experiment > cannot depend on the labels attached. What axiom of "Gedanken-experiment" theory does labeling violate? Suppose instead of labels on the balls one has balls of differing radii, so that the ball of label n is replaced by a ball of radius (n-1)/n. Is there also an axiom of "Gedanken-experiment" theory that prohibits using different sized balls? > Further the first result is incorrect if the fact is observed that the > number of balls in A increases continuously. So we have the result: At > noon all balls are out of A, but in A there are not less (even some > more) balls than outside. This is exactly what I call a silly (i.e. > unserious) result. Those that insist that mathematics limit itself to applications to some sort of physical reality will find most of mathematics off limits.
From: Virgil on 6 Oct 2006 15:25 In article <1160126832.709755.186110(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > That is nothing more than opinion and taste. But that is not a disproof of > > the proof given. > > Of course. There cannot be a disproof, because a disproof would not be > a disproof. If no disproof is possible, the proof must be valid. > > Your reaction shows me why set theory can never be conradicted. It is a > religion. No more of a religion than what "Mueckenh" has been preaching.
From: Randy Poe on 6 Oct 2006 17:06 Randy Poe wrote: [many times] > That didn't answer the question. In which one did your > version of the axiom of infinity occur? Sorry about all that. Google kept telling me there was a server error, the message didn't post and to try again. - Randy
From: Lester Zick on 6 Oct 2006 19:10
On Fri, 06 Oct 2006 12:57:16 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <1160123095.800410.99250(a)m7g2000cwm.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > >> Virgil schrieb: >> >> > In article <1160044514.105544.245260(a)c28g2000cwb.googlegroups.com>, >> > mueckenh(a)rz.fh-augsburg.de wrote: >> > >> > > Dik T. Winter schrieb: >> > > >> > > >> > > > > > > (There are exactly twice >> > > > > > > so >> > > > > > > much >> > > > > > > natural numbers than even natural numbers.) >> > > > > > >> > > > > > By what definitions? You never state definitions. >> > > > > >> > > > > By the only meaningful and consistent definition: A n eps |N : >> > > > > |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}|. >> > > > > Do you challenge its truth? >> > > > >> > > > No, I never did. But you draw conclusions about it about the set N. >> > > > Indeed, >> > > > for each finite n, it is true. >> > > >> > > And N is nothing but the collection of all finite n. >> > >> > That does not require that what is true for every member of a set be >> > true for the set itself. >> > >> > {2,4,6} is an odd sized set, despite all its members being of even size. >> >> And Mars looks red although all Marsians are green. Such analogies do >> not prove anything. In particular a set of finite natural numbers >> cannot be infinite, because the sum of differences of 1 between these >> numbers also makes up a finite natural number, as long as only finite >> numbers are present in the set. > >No one but idiots like you and TO claim that having infinitely many >finite naturals requires having anything like an infinite natural. > >> But this sum is nothing than the number >> of numbers (less 1). > >The "number" of naturals is not a natural. So then is the number of naturals an "unnatural"? > And a "sum" such as the one >suggested, need not exist at all. ~v~~ |