Galileo's Paradox
in [Math]
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From: Tonico on 8 Dec 2006 15:18 Tony Orlow ha escrito: > You can call me a troll if that makes you feel better. You seem to need > to bolster your ego by piling it on top of others. Hopefully you'll work > that out eventually. I won't concern myself with your spiritual > development too deeply, but I do have some questions. ***************************************************** Lemme see: troll....yup, it makes me feel better....ah. ***************************************************** > What is your definition of "troll"? From what I understand, in this > context, it's someone who just wants to make inflammatory comments which > foment argument, someone who evaluates their performance based on the > number of responses they get. That's not necessarily an unworthy > endeavor, if the area you address is too complacent and needs stirring, > but what makes you think that's what I or Eckard are doing? Can you > really be so ignorant as to think there aren't major problems with set > theory in the transfinite arena, at least intuitively? Surely you must > see that defending the conclusions of the theory regresses into > defending pure deduction, as having complete priority over the inductive > process of establishing the axiomatic rules in the first place? The > question we both address and agree on is whether set theories axioms are > appropriate or applicable to anything real, when it comes to infinite > sets. Eckard is an anti-Cantorian, choosing like WM and others to reject > the very notion of an "infinite set" as inconsistent, since "infinite" > implies a process, and "set" implies something static, "set in stone". *************************************************************** Amazing ammount of nonsenses in such a short paragraph: you, and Eckie, are trolls because you both get into "debating" (let's calls it that...) something you both know bananas about. In the case of Eckie it gets even better because that idiot gets some rather weird pleasure from belitling and calling names to whoever accepts what he, and others, are just uncapable of understanding. He, and you and others, have already been said time after time that mathematics, and mathematicians, don't give half a damn whether you're mad and angry at something because you BELIEVE that something doesn't fit what you have decided is reality. As a matter of fact, even if there existed a widely accepted definition of what "reality" is, and EVEN if some parts of math doesn't fit in there, that's not reason to believe that mathematicians MUST change their rules of games within mathematics, and this is one of the toughest parts for some of you to understand: who ever told you, you weird, weird creatures, that mathematics MUST fit into reality, whatever that is?!? The increidibly dense stupidity of those not willing to see the above is what moves me, and perhaps others, to call you, Eckie, Mueck and others trolls...and cranks. There are some VERY simple definitions in set theory (either naive or ZF, AC or not), and some of them are REALLY as simple as one can expect: a set is called "infinite" if there exists a bijection (which already has been completely and fully WELL defined) between that set and at least one of its proper subsets. Period. That is all there is to it. You don't wanna accept this definition? Good, propose yours..."potencial infinity", "actual infinity", shminfinity: give us DEFINITIONS, axioms to work with...and let's hope that upon checking and re-checking, those axioms and definitions aren't shown to be inconsistent, which has NOT been proved for ZF, AC or not AC....and that they are sufficiently interesting to deal with, of course. I still wonder what is what pisses off so much some trolls about this: Eckie's anger against Dedekind in special is laughable, and one of the most interesting sides of a crank I've seen in the last years... After some time interchanging posts, some of these trolls/crankis begin to REALLY believe that they have proved inconsistencies, contradictions, etc. Just read some of Eckie's posts to see what a diet low in potassium can do to human brain. So the above, and very specially the despise and offensive tone many idiotic trolls/cranks use to refer to PROFESSIONAL mathematicians just because they don't abide by their whims is what makes me call you people what you are: trolls/cranks. And one last question from me to you: what do you think of my remark, some 5-6 days ago, that as far as I know, NONE of the megacranks is a mathematician? Don't you wonder about this? I don't doubt there are mathematicians that don't like this ir that part in math, but I bet they won't troll about it as you people do, and that's a huge difference. Tonio > That's not unreasonable, though too conservative for me, and so I look > for other ways to formulate "infinite" and "set", so that they can be > integrated with "measure". You may find it amusing that those that think > for themselves don't agree on everything like those that take their > answers from the same history books, and think it proves you are right > because you agree more. It's easy to agree, when you don't think for > yourself. > > What was your last discovery? > > TonyCo
From: Virgil on 8 Dec 2006 15:52 In article <4579b6a1$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <4575b508(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Eckard Blumschein wrote:(deleted) > > > >> Now, just a minute, Eckard. You're contradicting yourself > > > > If even TO is taking EB to task, then EB must indeed be in a bad skin. > > Eckard and I are discussing things. We can disagree. It's not like > either of us agrees with a comfortable majority. so do we lose much > security in disagreeing with each other? Some of us are used to being > insecure, and yet, strong, and persisting, and surviving. I have a funny > feeling you did that, socially, during a period.... Life's like that. > > M. Antoni Your purely social comments have no mathematical relevance.
From: Virgil on 8 Dec 2006 15:57 In article <4579bc95(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > What,in mathematics, has a solution which is neither a real measure, or > the measure of truth of a statement, 0, 1, or somewhere in between? > Measure=maths. In grade schools "Math" may appear to be just "problems" whose "solutions" you are supposed to find, but that is a puerile view.
From: Tony Orlow on 8 Dec 2006 15:58 Tonico wrote: > Tony Orlow ha escrito: > >> You can call me a troll if that makes you feel better. You seem to need >> to bolster your ego by piling it on top of others. Hopefully you'll work >> that out eventually. I won't concern myself with your spiritual >> development too deeply, but I do have some questions. > > ***************************************************** > Lemme see: troll....yup, it makes me feel better....ah. > ***************************************************** > Well, that's very nice for you and your diminutive ego.... >> What is your definition of "troll"? From what I understand, in this >> context, it's someone who just wants to make inflammatory comments which >> foment argument, someone who evaluates their performance based on the >> number of responses they get. That's not necessarily an unworthy >> endeavor, if the area you address is too complacent and needs stirring, >> but what makes you think that's what I or Eckard are doing? Can you >> really be so ignorant as to think there aren't major problems with set >> theory in the transfinite arena, at least intuitively? Surely you must >> see that defending the conclusions of the theory regresses into >> defending pure deduction, as having complete priority over the inductive >> process of establishing the axiomatic rules in the first place? The >> question we both address and agree on is whether set theories axioms are >> appropriate or applicable to anything real, when it comes to infinite >> sets. Eckard is an anti-Cantorian, choosing like WM and others to reject >> the very notion of an "infinite set" as inconsistent, since "infinite" >> implies a process, and "set" implies something static, "set in stone". > > *************************************************************** > Amazing ammount of nonsenses in such a short paragraph Yes, be amazed, and now make sense of it... : you, and Eckie, > are trolls because you both get into "debating" (let's calls it > that...) something you both know bananas about. Bunches of stuff? In the case of Eckie it > gets even better because that idiot gets some rather weird pleasure > from belitling and calling names to whoever accepts what he, and > others, are just uncapable of understanding. Oh, I've enjoyed that myself.... > He, and you and others, have already been said time after time that > mathematics, and mathematicians, don't give half a damn whether you're > mad and angry at something because you BELIEVE that something doesn't > fit what you have decided is reality. I never said that, but do go on.... As a matter of fact, even if > there existed a widely accepted definition of what "reality" is, and > EVEN if some parts of math doesn't fit in there, that's not reason to > believe that mathematicians MUST change their rules of games within > mathematics, and this is one of the toughest parts for some of you to > understand: who ever told you, you weird, weird creatures, that > mathematics MUST fit into reality, whatever that is?!? When there is a balance between one assumption and another, we are in a position to justify one or the other. That's logic.... > The increidibly dense stupidity of those not willing to see the above > is what moves me, and perhaps others, to call you, Eckie, Mueck and > others trolls...and cranks. "Incredibly dense stupidity" - I don't suppose you're being at all prejudgidicial? > There are some VERY simple definitions in set theory (either naive or > ZF, AC or not), and some of them are REALLY as simple as one can > expect: a set is called "infinite" if there exists a bijection (which > already has been completely and fully WELL defined) between that set > and at least one of its proper subsets. Period. That is all there is to > it. Cardinality, yes, is simplistic - no argument. Very simplistic... > You don't wanna accept this definition? Good, propose > yours..."potencial infinity", "actual infinity", shminfinity: give us > DEFINITIONS, axioms to work with...and let's hope that upon checking > and re-checking, those axioms and definitions aren't shown to be > inconsistent, which has NOT been proved for ZF, AC or not AC....and > that they are sufficiently interesting to deal with, of course. Okay, a "potential" infinite set is one where each element, like the naturals, has a specific string associated with it, which has a left-hand end. > I still wonder what is what pisses off so much some trolls about this: > Eckie's anger against Dedekind in special is laughable, and one of the > most interesting sides of a crank I've seen in the last years... > After some time interchanging posts, some of these trolls/crankis begin > to REALLY believe that they have proved inconsistencies, > contradictions, etc. Just read some of Eckie's posts to see what a diet > low in potassium can do to human brain. No one here claims any such thing. One can only claim that certain logical constructions involved are invalid. You can dismiss it as a nutritive deficiency, but that may be on your own part... > So the above, and very specially the despise and offensive tone many > idiotic trolls/cranks use to refer to PROFESSIONAL mathematicians just > because they don't abide by their whims is what makes me call you > people what you are: trolls/cranks. There is nothing wrong with expecting science to satisfy intuition. > And one last question from me to you: what do you think of my remark, > some 5-6 days ago, that as far as I know, NONE of the megacranks is a > mathematician? Don't you wonder about this? I don't doubt there are > mathematicians that don't like this ir that part in math, but I bet > they won't troll about it as you people do, and that's a huge > difference. > Tonio > > > I chose to work within computer science, after having planned to become a mathematician, for the obvious reasons.... >> That's not unreasonable, though too conservative for me, and so I look >> for other ways to formulate "infinite" and "set", so that they can be >> integrated with "measure". You may find it amusing that those that think >> for themselves don't agree on everything like those that take their >> answers from the same history books, and think it proves you are right >> because you agree more. It's easy to agree, when you don't think for >> yourself. >> >> What was your last discovery? >> >> TonyCo > No anwswer? Hmmm. Why does 2's complement work? Can you explain that? I can. TonyCo
From: Tony Orlow on 8 Dec 2006 15:59
stephen(a)nomail.com wrote: > Six wrote: >> On 6 Dec 2006 07:08:46 -0800, "Mike Kelly" <mk4284(a)bris.ac.uk> wrote: > >>> Six wrote: >>>> I am very grateful to you for expanding on this. While I'm almost >>>> certain I'm missing something, I'm afraid I still don't get it. >>>> >>>> How exactly does claiming that a 1:1 C is not necessarily >>>> indicative of equality of size with infinite sets presuppose an inability >>>> to map (eg) the binary and decimal representations of integers? >>>> >>>> There is still a 1:1 C between the two sets. It is still true that >>>> for any finite sets a 1:1C implies equality of size. Moreover it's still >>>> reasonable to suppose that a 1:1C implies equality of size in the infinite >>>> case unless there are other, 'functional' reasons to the contrary. (Vague, >>>> I know. Roughly, 1:1 C is a necessary but not sufficient condition for >>>> equality of size.) >>>> >>>> The idea is that the naturals (in any base) form a paradigm or >>>> norm, a standard against which other sets can be measured. >>> The set of finite binary strings is a subset of the set of finite >>> decimal strings. > >> I confess I hadn't fully appreciated this simple point, that >> together with the fact that the strings just are, so to speak, the natural >> numbers (in a given base). > >>> Then b) precludes them being the same size. >>> >>> They are also both the same size as the set of natural numbers. >>> >>> Thus they are the same size as each other. >>> >>> Contradiction. > >> One is driven to the conclusion that there is no base-independent >> size for the natural numbers. > > How can the size be base dependent? The natural numbers are not base dependent. > Any natural number can be expressed in any base. There is no natural number > expressible in base 16 that is not expressible in base 10, or base 9, or base 2. > > I suppose you could claim that there is a set of decimal numbers, and a set > of base 2 numbers, and a set of hexadecimal numbers, and that they are all > different, and all have different sizes. But it is a strange notion of > "different size" given that all the sets represent the same thing. > > Stephen Measure is something different from the language needed to express it. |