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From: albstorz on 22 Oct 2005 11:53 Daryl McCullough wrote: > > No, the number of finite sets of finite naturals is exactly > the same as the number of finite naturals. 2^N is the number > of *all* subsets, including infinite and finite subsets. Yes, > I know you think that N is finite, but you are an idiot. I'm really interested to know, what you are think: what is the result of 2*N. 2*N = ? Please. regards AS
From: albstorz on 22 Oct 2005 12:00 David R Tribble wrote: > Albrecht Storz wrote: > >> So, if there is an infinite set there is an infinite number. > > > > David R Tribble wrote: > >> Do you mean that an infinite set (or natural numbers) must contain an > >> infinite number as a member (which is false)? Or do you mean that > >> the size of an infinite set is represented by an infinite number > >> (which is partially true)? > > > > Albrecht Storz wrote: > > Not only partially. If there is no infinite number there is no infinite > > set. > > If sets consist of discret, distinguishable, individual elements, and > > sets are definde like this, the natural numbers are just representative > > for the elements and also for the sets. > > {1,2,3} means a set with element #1, element #2, element #3, this is > > the ordinal aspect of numbers. The set with cardinality 3 is just this > > set {1,2,3}, and at the same time it represents all sets with 3 > > elements. That's the open secret of the numbers. > > > > ordinal = cardinal = natural > > Only for finite sets or numbers. > > For infinite sets we must use infinite ordinals and infinite > cardinals. But these ordinals and cardinals do not equate to any > naturals because there are no infinite natural numbers. Yes. And the cause of this aspect is very good: there are no infinite sets in the sense of a size. Infinite means just: sizeless big. Modern math calls this aleph_0. ok. but you can do nothing with this. Else you will earn contradictions. > > What is the number for set N = {0,1,2,3,...}? There is no number. > If it's w, then how can w be a member of N? what is "w"? Nothing more than "unicorn". > If it's w+1, then how can w+1 be a member of N? .... > If it's w-1 (whatever that means), then how can w-1 be a member of N? Whatever this means? Nothing. Regards AS
From: albstorz on 22 Oct 2005 12:15 Daryl McCullough wrote: > albstorz(a)gmx.de says... > > >You can biject all constructable subsets of P(N) to N, but not the > >unconstructable. > > By "constructable" do you mean "definable"? Or do you mean "computable"? > Or do you mean "finite", or what? Let's have a deal: By unconstructable I mean "Unconstructable". May be. > > Let me list the combinations here: > > 1. There is no bijection between N and the set of all subsets of N. > 2. There is no computable bijection between N and > the set of all computable subsets of N. > 3. There is no definable bijection between N and the > set of all definable subsets of N. > > Whatever notion of function we want, it is true that there > is no function mapping N to the set of all functions from > N into {0,1}. No. You are just kidding? Nothing of this is truth. > > However, if you mix your notions of functions, you can > get mixed results: > > 2'. There *is* a definable bijection between N and the > set of all computable subsets of N, but that bijection > is not computable. > > 3'. There *is* a bijection between N and the set of all > definable (in the language of arithmetic) subsets of N, > but that bijection is not definable in the language of > arithmetic. > > 3' can be extended further: > > 3''. There *is* a bijection between N and the set of all > definable (in the language of ZFC) subsets of N, but > that bijection is not definable in the language of ZFC. > > If you stick to any one consistent notion of "function" and > "subset", then Cantor's theorem tells you that there is no > bijection (according to that notion) between N and the set of > subsets (according to that notion) of N. > > -- > Daryl McCullough > Ithaca, NY Oh, it's just mindfucking, nothing more. Show me one computable infinite subset of N. In totally. Cantor's dream leads to a nondenumerable mass of schwachsinn. Nothing more. Regards AS
From: Virgil on 22 Oct 2005 14:49 In article <1129994377.366391.296970(a)g49g2000cwa.googlegroups.com>, albstorz(a)gmx.de wrote: > David R Tribble wrote: > > Albrecht Storz wrote: > > > So, if there is an infinite set there is an infinite number. > > > > Do you mean that an infinite set (or natural numbers) must contain an > > infinite number as a member (which is false)? Or do you mean that > > the size of an infinite set is represented by an infinite number > > (which is partially true)? > > > Depending on the axiomatic construction and depending on the necessary > of truth (since truth means logic consequence) either there are > infinite natural numbers or there is no infinite set. > > > Regards > AS A system capable of containing "inifitely many" finite natural numbers need not contain anything else but finite natural numbers.
From: Virgil on 22 Oct 2005 14:50
In article <1129994589.163116.238410(a)g14g2000cwa.googlegroups.com>, albstorz(a)gmx.de wrote: > Virgil wrote: > > In article <1129946611.902596.262670(a)g49g2000cwa.googlegroups.com>, > > "William Hughes" <wpihughes(a)hotmail.com> wrote: > > > > > Dave Rusin wrote: > > > > In article <1129901285.084347.34810(a)g49g2000cwa.googlegroups.com>, > > > > William Hughes <wpihughes(a)hotmail.com> wrote: > > > > > > > > >Yes all sets have a cardinality. > > > > > > > > That's your Choice. > > > > > > Am I assuming AC here? > > > > > > My understanding was that, while AC was needed to > > > put a total ordering on the equivalence classes > > > under bijection, one could assert the existence > > > of these classes even without AC. Or are the > > > cardinalities defined not as all possible > > > equivalence classes but as the equivalence classes > > > on the ordinals? > > > > > > -William Hughes > > > > As I understand it, without AC, one cannot be sure of creating any sort > > of function at all from one arbitrary set to another, much less > > guarantee that such a function, even if creatable, be an injection or a > > surjection. > > > Modern math concept leads to garbage thinking. > > > Regards > AS As AS does't seem to be able to think at all, it can make no difference to him what kind of thinking is involved. |