The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: PD on 24 Mar 2007 14:43 On Mar 23, 6:01 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 23 Mar 2007 12:33:46 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: > > > > >On Mar 22, 6:04 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: > > >> >On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> >> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> > >> >> wrote: > >> >> >Lester Zick wrote: > >> >> >> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowh...(a)nowhere.com> > >> >> >> wrote: > > >> >> >>> Tony Orlow wrote: > >> >> >>>> There is no correlation between length and number of points, because > >> >> >>>> there is no workable infinite or infinitesimal units. Allow oo points > >> >> >>>> per unit length, oo^2 per square unit area, etc, in line with the > >> >> >>>> calculus. Nuthin' big. Jes' give points a size. :) > >> >> >>> Points (taken individually or in countable bunches) have measure zero. > > >> >> >> They probably also have zero measure in uncountable bunches, Bob. At > >> >> >> least I never heard that division by zero was defined mathematically > >> >> >> even in modern math per say. > > >> >> >> ~v~~ > > >> >> >Purrrrr....say! Division by zero is not undefinable. One just has to > >> >> >define zero as a unit, eh? > > >> >> A unit of what, Tony? > > >> >> >Uncountable bunches certainly can attain nonzero measure. :) > > >> >> Uncountable bunches of zeroes are still zero, Tony. > > >> >Why no, no they're not, Lester. > > >> Of course you say so, Draper. Fact is that uncountable bunches of > >> infinitesimals are not zero but non uncountable bunches of zeroes are. > > >> >Perhaps a course in real analysis would be of value. > > >> And perhaps a course in truth would be of value to you > > >Absolutely. And who would you propose teach it? > > Moi? See below. > > > Do you have any truth > >to teach? If so, pray tell, where is it? > > Wherever. Pray tell when you learn to pay attention in class instead > of just running your mouth. Gladly, just as you as you bring forth the truth you say you are teaching. Where is it? > > >> unless of > >> course you wish to maintain that division by zero is defined even in > >> neomethematics. > > >Did I say that? > > What difference does that make/ It makes for good reading especially > when replying to the posts of others. Ah. It's all about the dance, isn't it, Lester. Screw the truth. You've got dancing to do. > > > And how is this related to the statement that an > >uncountable bunch of zeroes can have nonzero measure? > > Beats me. I was hoping you might not be paying attention. That clearly is what you hope happens most of the time you post. You apparently only talk to hear yourself do it. > You rarely > do particularly when a reply is addressed to you. There you go again, Lester, making the conclusion that a problem on your end is instead the result of someone else's choices. > Clearly you imagine > uncountable bunches of zeroes can have nonzero measure. But then > imagination is what you make of it. > > >> >Ever consider reading, rather than just making stuff up? > > >> No. > > >Ah, well, there's THAT approach, I suppose. > > Sauce for the goose I suppose. A goose you are, then, by self-proclamation.
From: Virgil on 24 Mar 2007 14:51 In article <1174761803.207342.288890(a)p15g2000hsd.googlegroups.com>, "PD" <TheDraperFamily(a)gmail.com> wrote: > On Mar 23, 6:01 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > > On 23 Mar 2007 12:33:46 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: > > > > > > > > >On Mar 22, 6:04 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > > >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: > > > > >> >On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > > >> >> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> > > >> >> wrote: > > >> >> >Lester Zick wrote: > > >> >> >> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker > > >> >> >> <nowh...(a)nowhere.com> > > >> >> >> wrote: > > > > >> >> >>> Tony Orlow wrote: > > >> >> >>>> There is no correlation between length and number of points, > > >> >> >>>> because > > >> >> >>>> there is no workable infinite or infinitesimal units. Allow oo > > >> >> >>>> points > > >> >> >>>> per unit length, oo^2 per square unit area, etc, in line with > > >> >> >>>> the > > >> >> >>>> calculus. Nuthin' big. Jes' give points a size. :) > > >> >> >>> Points (taken individually or in countable bunches) have measure > > >> >> >>> zero. > > > > >> >> >> They probably also have zero measure in uncountable bunches, Bob. > > >> >> >> At > > >> >> >> least I never heard that division by zero was defined > > >> >> >> mathematically > > >> >> >> even in modern math per say. > > > > >> >> >> ~v~~ > > > > >> >> >Purrrrr....say! Division by zero is not undefinable. One just has to > > >> >> >define zero as a unit, eh? > > > > >> >> A unit of what, Tony? > > > > >> >> >Uncountable bunches certainly can attain nonzero measure. :) > > > > >> >> Uncountable bunches of zeroes are still zero, Tony. > > > > >> >Why no, no they're not, Lester. > > > > >> Of course you say so, Draper. Fact is that uncountable bunches of > > >> infinitesimals are not zero but non uncountable bunches of zeroes are. > > > > >> >Perhaps a course in real analysis would be of value. > > > > >> And perhaps a course in truth would be of value to you > > > > >Absolutely. And who would you propose teach it? > > > > Moi? > > See below. > > > > > > > > > Do you have any truth > > >to teach? If so, pray tell, where is it? > > > > Wherever. Pray tell when you learn to pay attention in class instead > > of just running your mouth. > > Gladly, just as you as you bring forth the truth you say you are > teaching. Where is it? > > > > > >> unless of > > >> course you wish to maintain that division by zero is defined even in > > >> neomethematics. > > > > >Did I say that? > > > > What difference does that make/ It makes for good reading especially > > when replying to the posts of others. > > Ah. It's all about the dance, isn't it, Lester. Screw the truth. > You've got dancing to do. > > > > > > And how is this related to the statement that an > > >uncountable bunch of zeroes can have nonzero measure? > > > > Beats me. I was hoping you might not be paying attention. > > That clearly is what you hope happens most of the time you post. You > apparently only talk to hear yourself do it. > > > You rarely > > do particularly when a reply is addressed to you. > > There you go again, Lester, making the conclusion that a problem on > your end is instead the result of someone else's choices. > > > > Clearly you imagine > > uncountable bunches of zeroes can have nonzero measure. But then > > imagination is what you make of it. > > > > >> >Ever consider reading, rather than just making stuff up? > > > > >> No. > > > > >Ah, well, there's THAT approach, I suppose. > > > > Sauce for the goose I suppose. > > A goose you are, then, by self-proclamation. The only proper response to a Zick posting is killfiling him.
From: Lester Zick on 24 Mar 2007 15:19 On Sat, 24 Mar 2007 08:00:17 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 22 Mar 2007 20:15:37 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Thu, 22 Mar 2007 17:15:35 -0500, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <tony(a)lightlink.com> >>>>>> wrote: >>>>>> >>>>>>> Lester Zick wrote: >>>>>>>> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowhere(a)nowhere.com> >>>>>>>> wrote: >>>>>>>> >>>>>>>>> Tony Orlow wrote: >>>>>>>>>> There is no correlation between length and number of points, because >>>>>>>>>> there is no workable infinite or infinitesimal units. Allow oo points >>>>>>>>>> per unit length, oo^2 per square unit area, etc, in line with the >>>>>>>>>> calculus. Nuthin' big. Jes' give points a size. :) >>>>>>>>> Points (taken individually or in countable bunches) have measure zero. >>>>>>>> They probably also have zero measure in uncountable bunches, Bob. At >>>>>>>> least I never heard that division by zero was defined mathematically >>>>>>>> even in modern math per say. >>>>>>>> >>>>>>>> ~v~~ >>>>>>> Purrrrr....say! Division by zero is not undefinable. One just has to >>>>>>> define zero as a unit, eh? >>>>>> A unit of what, Tony? >>>>>> >>>>>>> Uncountable bunches certainly can attain nonzero measure. :) >>>>>> Uncountable bunches of zeroes are still zero, Tony. >>>>>> >>>>>> ~v~~ >>>>> Infinitesimal units can be added such that an infinite number of them >>>>> attain finite sums. >>>> And since when exactly, Tony, do infinitesimals equal zero pray tell? >>>> >>>> ~v~~ >>> Only in the "standard" universe, Lester. >> >> So 1-1="infinitesimal" Tony? Somehow I doubt that's exactly what >> Newton and Leibniz had in mind with their calculus. >> >> ~v~~ > > 1=0.999...? Well, Tony, 0.999 . . . is only an approximation to 1 and not 1 per se. However it's still the case that 0.999 . . . - 0.999 . . . = 0 and not some infinitesimal magnitude. Now as to your underlying contention that "uncountable bunches of zeroes can attain nonzero measure" by which I assume you mean finite measure since zero itself is finite, division of finites by zero would have to be defined for this to be possible.My reasoning is as follows. Let's assume we have some uncountable bunch of zeroes U and U*0 equals some nonzero magnitude X. Thus U*0=X where I suppose X might equal a finite cardinal like three.At least this is how I interpret the claim. So I suppose the next contention would concern whether the operation is reversible and whether we could calculate U=3/0? If so 3/0 would have to be defined and I don't see it is in any kind of formal math. I expect there are a couple different ways you might get around the problem. You might try to define 3/0 in some way compatible with your basic contention, for example claim that the operation involved is not reversible. Or you might claim U*0 is an infinitesimal of some kind and not finite at all. Or you might try to establish U as some kind of weird uncountable not exactly related to counting. Or you might try to suggest that "*" and "/" are not the common garden variety operations we expect in ordinary math. However I think whichever route you take you have to do considerably more than simply make a claim like the one you did because all these considerations are inextricably linked. Nor is it readily apparent what the objective of all this might be. I understand what you seem to be after with the +00-00 number ring and all. But what's the point of all this if you have to corrupt the very concepts you're trying to unite to do it? I mean we already have the transfinite SOAP opera nonsense which has had to corrupt the meanings of points and lines and points as constituents of lines, straight lines, curves, irrationals, transcendentals, and so on to achieve its aims of explaining geometry arithmetically.I just don't see the point. It looks to me as if mathematikers expect they can unite disparate mathematical functions with a wink and a nod through some kind of nomenclatural legerdemain such as simply calling lead gold and pretending to have found the philosophers stone. The problem is then mathematikers have to invent all kinds of private terminologies and regressional linguistic subterfuges, more commonly known as dodges, to circumvent an obvious implication that they really haven't done what they claimed. I've seen exactly analogous strategems in psychology and artificial intelligence. Instead of actually solving problems in the disciplines behaviorists and computer programmers quietly under the cover of darkness exchange one set of problems which they can't explain for another which they can or at least plausibly pretend they can. Then they have to defend their evasions with the silliest terminological regressions and excuses imaginable. The result is a vast network of language and terminology designed to obfuscate the unitiated instead of answering questions. It's always been the same with every faith based mystical epistemology. A priestly caste emerges to guide believers in the faith with rote catechisms and dogma whose actual rationales are safely cloaked and closeted within ivory towers. Requiescant in pace. ~v~~
From: Lester Zick on 24 Mar 2007 18:42 On 24 Mar 2007 11:43:23 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 23, 6:01 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On 23 Mar 2007 12:33:46 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: >> >> >> >> >On Mar 22, 6:04 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: >> >> >> >On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> >> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> >> >> >> wrote: >> >> >> >Lester Zick wrote: >> >> >> >> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowh...(a)nowhere.com> >> >> >> >> wrote: >> >> >> >> >>> Tony Orlow wrote: >> >> >> >>>> There is no correlation between length and number of points, because >> >> >> >>>> there is no workable infinite or infinitesimal units. Allow oo points >> >> >> >>>> per unit length, oo^2 per square unit area, etc, in line with the >> >> >> >>>> calculus. Nuthin' big. Jes' give points a size. :) >> >> >> >>> Points (taken individually or in countable bunches) have measure zero. >> >> >> >> >> They probably also have zero measure in uncountable bunches, Bob. At >> >> >> >> least I never heard that division by zero was defined mathematically >> >> >> >> even in modern math per say. >> >> >> >> >> ~v~~ >> >> >> >> >Purrrrr....say! Division by zero is not undefinable. One just has to >> >> >> >define zero as a unit, eh? >> >> >> >> A unit of what, Tony? >> >> >> >> >Uncountable bunches certainly can attain nonzero measure. :) >> >> >> >> Uncountable bunches of zeroes are still zero, Tony. >> >> >> >Why no, no they're not, Lester. >> >> >> Of course you say so, Draper. Fact is that uncountable bunches of >> >> infinitesimals are not zero but non uncountable bunches of zeroes are. >> >> >> >Perhaps a course in real analysis would be of value. >> >> >> And perhaps a course in truth would be of value to you >> >> >Absolutely. And who would you propose teach it? >> >> Moi? > >See below. > >> >> > Do you have any truth >> >to teach? If so, pray tell, where is it? >> >> Wherever. Pray tell when you learn to pay attention in class instead >> of just running your mouth. > >Gladly, just as you as you bring forth the truth you say you are >teaching. Where is it? Well you know you really need to pay attention in class, Draper. >> >> unless of >> >> course you wish to maintain that division by zero is defined even in >> >> neomethematics. >> >> >Did I say that? >> >> What difference does that make/ It makes for good reading especially >> when replying to the posts of others. > >Ah. It's all about the dance, isn't it, Lester. Screw the truth. >You've got dancing to do. Your sentiments exactly. You ask questions. I answer questions. What is it you're afraid of? Or more to the point what is it that you're not afraid of? >> > And how is this related to the statement that an >> >uncountable bunch of zeroes can have nonzero measure? >> >> Beats me. I was hoping you might not be paying attention. > >That clearly is what you hope happens most of the time you post. You >apparently only talk to hear yourself do it. Not much else to do when I'm right and you're not. Which experiment does your family propose exactly? >> You rarely >> do particularly when a reply is addressed to you. > >There you go again, Lester, making the conclusion that a problem on >your end is instead the result of someone else's choices. Which problem on my end did you have in mind exactly? >> Clearly you imagine >> uncountable bunches of zeroes can have nonzero measure. But then >> imagination is what you make of it. >> >> >> >Ever consider reading, rather than just making stuff up? >> >> >> No. >> >> >Ah, well, there's THAT approach, I suppose. >> >> Sauce for the goose I suppose. > >A goose you are, then, by self-proclamation. Yadayada whatever. Ask a stupid question you get a stupid answer. You got a stupid answer to your stupid question. Talk is frugal and you're cheap. ~v~~
From: Lester Zick on 24 Mar 2007 18:44
On Sat, 24 Mar 2007 12:51:51 -0600, Virgil <virgil(a)comcast.net> wrote: >The only proper response to a Zick posting is killfiling him. Sticks and stones . . . etc. Virgil is afraid of nothing except his own shadow. ~v~~ |