infinity ...
in [Math]
|
Prev: math
Next: The proof of mass vector.
From: David R Tribble on 17 Oct 2005 18:43 zuhair said: >> The number of # when n=w is simply= [(w^2)/2]+ w/2 > Tony Orlow wrote: > Gee, that looks amazingly similar to (N^2+N)/2 (my version) or N(N+1)/2 > (Martin's version). Fancy that. We all got the same answer for the sum of the > naturals! Is this a monkey-typewriter-shakespeare phenomenon? Okay, so the triangular number T(n) = n(n+1)/2, which is certainly true for any finite n. So what? Just because someone agrees with you doesn't make you right. It's not in the least bit surprising that all of you got the same answer by making the same incorrect assumptions. Fancy that. None of you three (or four, depending on the counting) have proven that infinite naturals must exist, and certainly none of you has proven that arithmetic with infinite numbers works the same as finite arithmetic.
From: Virgil on 17 Oct 2005 22:43 In article <MPG.1dbdd9753974682498a4c2(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > David R Tribble said: > > > For that to be true, there must be a bijection between an infinite > > set (any infinite set) and its powerset. Bitte, show us a > > bijection between N and P(N). > > > > > I already showed you the bijection between binary *N and P(*N). What > didn't you like about it? It is valid. There are at least two things wrong with it. (1) It is not valid by any standard mathematics or logic (only in TOmatics which is irrelevant to both standard logic and mathematics). (2) Unless *N is bijectable with N, no such bijection on N* is relevant to bijections on N.
From: albstorz on 18 Oct 2005 03:54 David R Tribble wrote: > Albrecht S. Storz wrote: > >> [...] > >> Since there is no biggest number and since there is no infinite number, > >> the size of the set of numbers in form of sets of #s is undefined as > >> the biggest natural number is undefined. > >> > >> But the sequence of the sets of # fullfill the peano axiomes. So this > >> set must be infinite. > >> > >> The cardinality of a set is not able to be infinite and "not defined" > >> at the same time. > >> This is the contradiction. > > > > David R Tribble wrote: > >> I don't see the contradiction. The size of the set is "not defined" > >> to be the same as any natural number, and the set size is obviously > >> infinite. This is no contradiction, since no natural number is > >> infinite. > >> > >> The thing that is "not defined" is the largest natural, which obviously > >> does not exist. But the set size is infinite, and is nicely defined > >> by an infinite cardinal. > >> > >> You seem to be mixing the two concepts of "natural" and "cardinal" > >> numbers to create a supposed contradiction, but that does not work. > > > > Albrecht S. Storz wrote: > > You are not able to understand that there is no difference between > > numerals and sets. > > I have no problem seeing the correspondence between natural numbers > and von Neumann sets. But neither of these are the same as > cardinalities, which are not numbers, but measures (sizes) of sets. You can not see, that in my demonstration there is no distinguishing betwéen sets, naturals, cardinalities. You can not see, that this, what holds for natural numbers must also holds for cardinalities. > > > > My sketches shows this exactly. > > Cantor proofs his wrong conclusion with the same mix of potential > > infinity and actual infinity. But there is no bijection between this > > two concepts. The antidiagonal is an unicorn. > > There is no stringend concept about infinity. And there is no aleph_1, > > aleph_2, ... or any other infinity. > > For that to be true, there must be a bijection between an infinite > set (any infinite set) and its powerset. Bitte, show us a bijection > between N and P(N). At first, you should show, that bijection means something to notwellordered infinite sets. Bijection is a clear concept on finite sets, it also works on wellordered infinite sets of the same infinite concept. Aber: Show me a bijection between two infinite sets with the same cardinality, where one of the sets is still not wellorderable. Than I will show you a bijection between N and P(N) or N and R or P(N) and P(P(N)) or what you want. But this is not the issue of this thread. You are free to critisize my, in the startposting demonstrated, argumentation. Regards AS
From: zuhair on 18 Oct 2005 05:11 David wrote: It's not in the least bit surprising that all of you got the same answer by making the same incorrect assumptions. Fancy that. ----------- Well although we reached into the same results, but their is some difference to me their is no number which can discribe the multiplicity of all natural numbers, but their are numbers which can discrible the sum of a specifically defined infinite sets of natural numbers. Examples: The sum of all natural numbers in N defined as N ={ 1,2,3,4,........} is: 1+2+3+4+............. = [(w^2)/2]+ w/2 But the sum of all natural numbers in Q defined as a set of natural numbers which has 2-1 correspondance with setN above : 246............ 135............ =Q Now the sum of numbers in Q is 2 4 6 + + + + + +.................. = [((2w)^2)/2]+ w = 2 w^2 + w 1 3 5 While the sum of all natural numbers for U where U has 3-1 correspondance with set N. is [((3w)^2)/2]+ 3w/2 In general the sum of all natural numbers in set X where X has a -1 correspondance with setN is: [((aw)^2)/2]+ aw/2 Best Zuhair
From: Tony Orlow on 18 Oct 2005 11:58
David R Tribble said: > Albrecht S. Storz wrote: > >> Cantor proofs his wrong conclusion with the same mix of potential > >> infinity and actual infinity. But there is no bijection between this > >> two concepts. The antidiagonal is an unicorn. > >> There is no stringend concept about infinity. And there is no aleph_1, > >> aleph_2, ... or any other infinity. > > > > David R Tribble said: > >> For that to be true, there must be a bijection between an infinite > >> set (any infinite set) and its powerset. Bitte, show us a bijection > >> between N and P(N). > > > > Tony Orlow wrote: > > I already showed you the bijection between binary *N and P(*N). > > What didn't you like about it? It is valid. > > No, you showed a mapping between *N and R, which is equivalent > to a mapping between *N and P(N). That's easy. No, it was specifically a bijection between two sets of infinite binary strings representing, on the one hand, the whole numbers in *N starting from 0, both finite and infinite, in normal binary format, and on the other hand, the specification of each subset of whole numbers in *N, where each bit which, in the binary number, represents 2^n denotes membership of n in the subset. This is a bijection between the whole numbers in *N and P(*N), using an intermediate bijection with a common set of infinite binary strings. This has nothing to do with the reals. Sorry. > > But you have not provided a mapping between any set and its powerset, > infinite or otherwise. Have too. > > -- Smiles, Tony |