The Definition of Points
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From: Virgil on 1 Apr 2007 01:02 In article <460f24eb(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460f1b3e(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <460ef839(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>> Virgil wrote: > >>>>> In article <460ee056(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>>> Please do expliculate what the contradiction is in an uncountable > >>>>>> sequence. What is true and false as a result of that concept? > >>>>> A mathematical sequence is a function with the naturals as domain. > >>>>> If TO wishes to refer to something which is not such a function, he > >>>>> should not refer to it as a sequence if he wishes to be understood in > >>>>> sci.math. > >>>>> > >>>>> > >>>> Pray tell, what term shall I use???? > >>> TO is so inventive in so many useless ways that I cannot believe that > >>> his imagination will fail him in such a trivially useful way. > >>>>>>> I know you are incapable of actually thinking about all the elements > >>>>>>> of > >>>>>>> N, > >>>>>>> but that is your problem. In any case, N is not an element of N. > >>>>>>> Citing Ross as support is practically an admission that you are > >>>>>>> wrong. > >>>>>>> > >>>>>>> Stephen > >>>>>>> > >>>>>> Sure, of course, agreeing with someone who disagrees with you makes me > >>>>>> wrong. I'll keep that in mind. Thanks.. > >>>>> > >>>>> It is not so much that Ross disagrees with one person, it is that he > >>>>> disagrees with everyone, frequently including himself. > >>>> Ross has a vision, even if not axiomatically expressed. In fact, he's > >>>> entirely honest about that, expounding an axiom free system. I like > >>>> Ross. So do you. Admit it. :) > >>>> > >>> > >>> Like Russell? > >>> > >>> What is there about him to like? > >> You don't like Russell? > > > > I don't know him well enough to like or dislike. I dislike his > > anti-mathematical idiocies. > > Define "mathematics" before you accuse anyone of being > "anti-mathematical". I doubt I agree with everything Russell said, but, > whatever. Never mind. Be as crotchety as you like. One definition might be the study of axiom systems and their consequences. Since Russell rejects all axiom systems, at least those of interest to mathematicians, he is anti-mathematical.
From: Virgil on 1 Apr 2007 01:11 In article <460f294b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > cbrown(a)cbrownsystems.com wrote: > >>> What does it mean for an ordering to be "discrete" or "linear"? What > >>> does it mean for something to "occur in" an ordering? > >> Linear means x<y ^ y<z ->x<z > > > > Funny; everyone else calls that "a transitive relation". > > Yes, is that unrelated? Since equality is a "linear relation" according to TO's definition, , TO must be requiring that equality be an ordering. > > > > > Let S = {a,b,c,f,g, h} > > > > Impose the following ordering: > > b < a > > c < b > > c < a > > f < a > > g < f > > g < a > > if x <> h, then h < x. > > > > The equivalent Hasse diagram: > > > > a > > / \ > > b f > > / \ > > c g > > \ / > > \ / > > \ / > > h > > > > This ordering satisfies, for all x,y,z in S: if x<y and y<z, then x<z. > > > > This is not what most people mean when they say "a linear ordering". > > Instead, it's an example of what people usually call a partial order. > > Okay, but that's an ordering that is based on some finite set of rules > regaring some finite set of points, which doesn't suffice to specify the > relationships between every pair of points. We can't say, from the > specified relationships, whether f<b or f<c or b<g or c<g. That's why > there's a parallel route, and so the diagram is "nonlinear". It could be > all on a line, but there would be several possible ordering given the > stated relationships. Nothing in TO's definition requires any more than "if x<y and y<z, then x<z", so that anything satisfying TO's definition must be, by his own standards, a linear ordering. On the other hand, TO could retract his insufficient definition and replace it with a valid one. > >>> So when you say "sequence" you're using an undefined term. As such, > >>> it's rather hard to your evaluate claims such as "There are actually > >>> infinite sequences". I have literally no idea what you are even trying > >>> to say. > >>> -- > >>> mike. > >> Oh gee, there has to be some word for it... > >> > > > > There almost certainly is; but as usual, it depends on what the /heck/ > > you're talking about. Perhaps the words "well-order" or "total order" > > actually already satisfy your requirements; or some particular proper > > subset of all non-isomorphic total orders satisfy your requirements. > > Or not. But how will you ever know if you refuse to /learn/ what these > > words refer to? > > > > Cheers - Chas > > > > I guess not by asking around here. Geeze. Those things have all been properly definied here so that TO's failure to learn them here is strictly his own fault.
From: Virgil on 1 Apr 2007 01:18 In article <460f2ac1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Let's examine what '<' means. x<y ^ y<z -> x<z. True for real > quantities, and true if '<' is taken to mean "is a proper subset of". > The proper subset is less than the whole, and the evens are half the > naturals. That's a very primitive result. This does not explain what "<" means. Perhaps TO needs to do a little work: http://en.wikipedia.org/wiki/Order_relation#Special_types_of_orders > > > > What I don't understand is what name you would like to give to the set > > {n : n e N and n <> N}. M? > > > > Cheers - Chas > > > > N-1? Why do I need to define that uselessness? Because if you can't do that, it is you that are useless.
From: stephen on 1 Apr 2007 01:21 In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: >> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >>> stephen(a)nomail.com wrote: >>>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: <snip> >> >>> Oh. What word shall I use? Supersequence? Is that related to a >>> subsequence or consequence? >> >> As long as you define your terms it does not matter to much what you >> call it. You could just call it an uncountably infinite sequence, but you >> need to define what that is if you want anyone to know what you are >> talking about. Why are you so reluctant to define your terms? >> > I did that, and was told no such thing exists. Gee, then, don't talk > about unicorns or alephs. Where did you define "uncountably infinite sequence"? Just naming it is not defining it. >>>>>>>>> If all other elements in the sequence are a finite number >>>>>>>>> of steps from the start, and w occurs directly after those, then it is >>>>>>>>> one step beyond some step which is finite, and so is at a finite step. >>>>>>>> So you think there are only a finite number of elements between 1 and >>>>>>>> w? What is that finite number? 100? 100000? 100000000000000000? >>>>>>>> 98042934810235712394872394712349123749123471923479? Which one? >>>>>>>> >>>>>>> Aleph_0, which is provably a member of the set, if it's the size of the >>>>>>> set. Of course, then, adding w to the set's a little redundant, eh? >>>>>> Aleph_0 is not a finite number. Care to try again? >>>>>> >>>>> It's also not the size of the set. Wake up. >>>> It is the cardinality of a set. >> >>> Is that a number? >> >> What is your definition of "number"? aleph_0 is called a transfinite >> number, but definitions, not names, are the important thing. >> > A number is a symbolic representation of quantity which can be > manipulated to produce quantitative results in the form of symbols. I > might be wrong, but I'm sure you can apprise me of the official meaning > of "number", mathematically. ;) And how does aleph_0 not fit that definition? Stephen
From: stephen on 1 Apr 2007 01:22
In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: >> >> None of the options mention "size" Tony. What does "size" have >> to do with a, b or c? >> > Ugh. Me already tell you, nth one is n, then there are n of them. So > easy, even a caveman can do it. Size is difference between. Brilliant Tony. Act like an idiot when backed into a corner. Did you learn that trick from Lester? You are truly pathetic. Stephen |