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From: Virgil on 22 Oct 2005 00:51 In article <MPG.1dc2fa9fc0584f2098a530(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > Virgil said: > > You failed to come up with any s in S such that > > f(s) = {x in S:x not in f(x)} > I failed to name the last natural? Shame on me! Why TO thinks that misrepresenting the issue of finding an s such that f(s) = {x in S:x not in f(x)} is connected to the issue of whether there is a last member of S will get him out of the fix he is in is just another of the mysteries continually surrounding the foggy land of TOmatica. > > > > > No one has been able to tell me, no matter how many times I > > > beg for assistance in understanding this deep and mysterious subject. > > > > To has been told, but his illiteracy prevents him from knowing it. > What rule of construction did I break in my bijection? What did I do wrong? It may have started with getting born. > > > > > > > > > If anyone counterclaims agains the proof of no surjection from and > > > > set X to its power set P(X), that person owes us an example of such > > > > a mapping. > > > > > And if anyone wants to claim their proof stands in the face of an > > > obvious counterexample, that person owes us an explanation of how > > > that counterexample does not apply. So, what of it, Virgie? > > > > It is TO claiming the counter-example to a standard proof. > > > > Let him find the counter-example, an S and a f:S -> P(S), > > and an s in S with f(s) = (x in S: x not in f(x)}. > 2^oo-1 maps to {0,...,oo-1}. Without knowing S and f, we cannot determine whether {0,...,oo-1} = {x in S:x not in f(x)} or not, so TO's answer is insufficient. > > > > > What rule > > > does my bijection between *N and P(*N) break? Take your time.... > > > > See above! > What did I do wrong, besides failing to name the last natural? Suggesting that there is one, for starters! > >
From: Virgil on 22 Oct 2005 00:55 In article <MPG.1dc2fb0061ec3e1e98a531(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > Virgil said: > > In article <MPG.1dc1ba6ecb69b51a98a514(a)newsstand.cit.cornell.edu>, > > Tony Orlow <aeo6(a)cornell.edu> wrote: > > > > > Virgil said: > > > > In article > > > > <1129721500.027651.21470(a)f14g2000cwb.googlegroups.com>, > > > > > > That shows how little AS knows about things, since given the > > > > axiom of choice, there is no such thing as a non-well-orderable > > > > set (though admittedly there are some sets known that have yet > > > > to be well-ordered). > > > > > > > Gee, like what, Virgil? > > > > Like one version of the axiom of choice, which merely states that > > every set is well-orderable, but gives no methodology for doing it. > > > Well, that sounds like rock-solid proof to me! Stupid arbitrary > axioms. Make it make sense. It is quite impossible to have things make sense while insulated from reality in the dream world of TOmatica. Until TO leaves that world, there are a lot of things that make perfect sense outside it that will not make sense to him.
From: Virgil on 22 Oct 2005 01:14 In article <MPG.1dc3059119c37f5d98a532(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > Actually, since I consider the set of finite naturals to be finite, > that number woudl have a finite number of bits and a finite value, > but anyway... But if an TO-finite set can be endless (TO-finite but unbounded ordered sets are endless as sequences), then a TO-finite string of bits is equally endless, and can be Dedekind infinite. TO continues to use "finite" and "infinite" in two different senses, sometime the Dedekind sense and sometimes the TO sense, without specifying which. Such deliberate ambiguity vitiates any meaning to statements by TO involving use of either "finite" or "infinite" without specific explanation of which sense ic meant. > > None of the standard proofs assume a last element. Just let it go. > It assumes a completed set with a completed string and a natural that > equals that string, corresponding to the completed set. For any > completion you consider, than number is beyond it. So, don't assume a > completion to the set. There is no such thing as an "uncompleted" set. the membership of any set is static. If a set exists at all it immutable. Any change in membership creates a new and different set. Thus, if x is not a member of set A, then A \/ {x}, where '\/' means union, is a different set. Similarly, if x is a member of set b, then B\{x}, where '\' means relative difference, is a different set. Where does To get this TOmatic notion that consants vary?
From: Virgil on 22 Oct 2005 01:37 In article <MPG.1dc3088a8b5b02f398a534(a)newsstand.cit.cornell.edu>, Tony Orlow <aeo6(a)cornell.edu> wrote: > Daryl McCullough said: > > Tony Orlow says... > > > > >Yes, your reiterations of the standard nonsense don't go very far > > >with me. > > > > That's because you are an idiot. You are incapable of formulating > > or understanding a mathematical argument. Worse, you believe > > yourself to be much more competent than you actually are. > So, you wanna go out for a beer, or what? LOL Didn't know they had bars in TOmatica. perhaps it is the bars in TOmatica that TO never leaves, and that is his problem. > > > > That's the point, really, of rigor and formalization. If you are > > speaking loosely, it's very easy to fool yourself into thinking you > > are making sense. But if you are forced to write down your > > reasoning in a careful, detailed, rigorous way, you will discover > > where your ideas are full of hot air. > Then perhaps they will fly. Not far, as such bubbles always burst quickly. > > > > Standard mathematics *has* gone through this process. Your junk has > > not. That's why standard mathematics is much higher quality than > > your bullshit. It's not because mathematicians have a higher IQ, > > but because they have a much stricter quality control process than > > you do. You have no quality control AT ALL. Even when you are > > confronted with an out-and-out contradiction in your ideas, it > > hardly fazes you---you don't change your ideas in the face of > > evidence that they are wrong, you just make up new weasel words > > like "tenuous existence", "unidentifiable naturals". > I express things the way I see them. Then TO needs a vision upgrade. > From your axiomatic standpoint, your arguments are airtight. Without an axiom system things cannot be airtight, that is the point of starting with an axiom system. We have a number of different axiom systems in all of which we have a Dedekind infinite set of (Dedekind finite) naturals from which we can build the usual number systems, calculus, etc., on which almost all modern mathematics, science and engineering is based. TO has no system of axioms, only some mutually- and self-contradictory intuitions which he can not make work in any system that requires adherence to the standard rules of logic. > From my perspective, they all rely on contorting a > very few paradoxical facts into general rules that defy reason. TO's "reason" defies logic. Most people, given the choice, will choose to defy TO and his "reason" before defying logic. > I don't expect you to see that. I also won't call you an idiot for > not seeing what is obvious to people like Martin, Zuhair, Ross, > myself and others. The difficulty with that group is that while they may publicly disagree with standard logic and mathematics, they do not entirely agree with each other, and occasionally even disagree with themselves. > > > > > The fact that you are not stupid makes your behavior all the worse: > > your idiocy is a *choice* on your part. You would rather be lazy > > and pretend to be doing mathematics than to work hard and > > *actually* do mathematics. > > Do you think it is lazy to try to construct a better foundation for > mathematics? If TO were trying to do that, he would not defy logic nor ignore logical arguments. Any "mathematics" in such defiance of logic is doomed to end up in a midden. Where it belongs.
From: Virgil on 22 Oct 2005 02:03
In article <djbihe$3l0$1(a)news.math.niu.edu>, rusin(a)vesuvius.math.niu.edu (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. At least if one chooses to have choice. |