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From: Tony Orlow on 18 Oct 2005 12:01 David R Tribble said: > 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. What incorrect assumptions? That the unending geometrical pattern continues and maintains the same constant relationships based on the definition of the geometrical pattern? What is your assumption? That it goes the way of the vase's balls, or that you can say whatever you fancy about it? > > 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. You can't make a horse drink. Stick your head in the bucket. You might find some oats as well. > > -- Smiles, Tony
From: Tony Orlow on 18 Oct 2005 12:03 Virgil said: > 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). Why, exactly. It's not a fly you can wave away. > > (2) Unless *N is bijectable with N, no such bijection on N* is relevant > to bijections on N. Accrding to you, it should be. You can certainly define a 1-1 correspondence between the elements, can't you? Where do you define the end of that relationship? That's irrelevant anyway. The point was making a bijection between a set and its power set. Again, Virgil misses the point. > -- Smiles, Tony
From: Virgil on 18 Oct 2005 13:15 In article <MPG.1dbee59ca85c4d9698a4c3(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > 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. > > > > But you have not provided a mapping between any set and its powerset, > > infinite or otherwise. > Have too. TO's delusions about what can represent what are not valid outside the twilight zone of TOmatics. TO simultaneously wants to represent each member of *N as (1) an infinite binary string, and (2) a one bit in one digit of an infinite binary string. Only in the twilight zone of TOmatics!
From: Virgil on 18 Oct 2005 13:22 In article <MPG.1dbee6776e2d5f7098a4c4(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > David R Tribble said: > > 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. > What incorrect assumptions? The first incorrect assumption you all made was that any of you have any abilities with either mathematics or logic at all. The second is that appending assumptions which are contradictory to the axiom systems they are being appended to improves those axiom systems. > That the unending geometrical pattern continues and maintains the > same constant relationships based on the definition of the > geometrical pattern? What is your assumption? That it goes the way of > the vase's balls, or that you can say whatever you fancy about it? One of our assumptions is that no ball remains in a vase after having been removed from it. TO obviously rejects this asumption. > > > > 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. > You can't make a horse drink. The end of the horse that we are addressing does not drink.
From: Virgil on 18 Oct 2005 13:39
In article <MPG.1dbee6e8ad3b615d98a4c5(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > Virgil said: > > 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). > Why, exactly. It's not a fly you can wave away. In standard mathematics, it has been proven that no bijection can exist between any set and its power set. So that if TO says that he has a bijection between some set and its power set, then, at least outside of the twilight zone of TOmatics, either that "set" is not a set (possibly a proper class), or the "power set" is not actually its power set or the "bijection" is not actually a bijection, or several of these. > > > > (2) Unless *N is bijectable with N, no such bijection on N* is relevant > > to bijections on N. > Accrding to you, it should be. Not by me, it isn't. For me N is the Dedekind infinite set of finite naturals representable by finite strings of digits in any natural base. By any reasonable standard, *most* members of TO's *N are not members of N. You can certainly define a 1-1 correspondence > between the elements, can't you? Between elements of what set and elements of what other set? Sometimes bijections do not exist, as, for example, between the empty set and any non-empty set. Between any standard version of N and TO's *N no bijection exists. > Where do you define the end of that > relationship? That's irrelevant anyway. The point was making a bijection > between a set and its power set. Again, Virgil misses the point. TO missed the point that, outside of the twilight zone of TOmatics, no bijection between any set and its power set is possible. What happens in that twilight zone of TOmatics is irrelevant to mathematics, as no proper mathematics can ever be done in a place where both every statement and its negation are theorems. |