The Definition of Points
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From: Lester Zick on 2 Apr 2007 17:39 On 2 Apr 2007 09:24:06 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: > Cardinality is bunk! Of course not. It just has nothing to do with SOAP operas. ~v~~
From: Tony Orlow on 12 Apr 2007 14:12 Lester Zick wrote: > On Sat, 31 Mar 2007 17:31:58 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On 30 Mar 2007 10:23:51 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >>> >>>> On Mar 30, 9:39 am, Tony Orlow <t...(a)lightlink.com> wrote: >>>> >>>>> They >>>>> introduce the von Neumann ordinals defined solely by set inclusion, >>>> By membership, not inclusion. >>>> >>>>> and >>>>> yet, surreptitiously introduce the notion of order by means of this set. >>>> "Surreptitiously". You don't know an effing thing you're talking >>>> about. Look at a set theory textbook (such as Suppes's 'Axiomatic Set >>>> Theory') to see the explicit definitions. >>> Kinda like Moe(x) huh. >>> >>> ~v~~ >> Welcome back to your mother-effing thread. :) > > What's interesting here, Tony, is the sudden explosion of interest in > a thread you commented only the other day appeared moribund. I mean > 200+ posts on any given Sunday may well be a record. > > I think the trick is that you have to confine posts pretty much to a > few sentences so mathematikers can read and respond to them whilst > moving their lips. I often suspected mathematikers only had verbal > IQ's about room temperature and the retention capacity of orangutans > and now we have empirical evidence to that effect. Probably why > they're modern mathematikers to begin with because their intellectual > skills appear fairly well limited to memorizing and repeating slogans. > > ~v~~ What may perhaps be more interesting is that, after I disappeared again for two weeks, the thread petered out again. The trickis actually pursuing a point that exists. :) 01oo
From: Tony Orlow on 12 Apr 2007 14:12 Lester Zick wrote: > On Sat, 31 Mar 2007 18:05:25 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Fri, 30 Mar 2007 12:06:42 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>> Lester Zick wrote: >>>>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>>>> wrote: >>>>> >>>>>>>> You might be surprised at how it relates to science. Where does mass >>>>>>>> come from, anyway? >>>>>>> Not from number rings and real number lines that's for sure. >>>>>>> >>>>>> Are you sure? >>>>> Yes. >>>>> >>>>>> What thoughts have you given to cyclical processes? >>>>> Plenty. Everything in physical nature represents cyclical processes. >>>>> So what? What difference does that make? We can describe cyclical >>>>> processes quite adequately without assuming there is a real number >>>>> line or number rings. In fact we can describe cyclical processes even >>>>> if there is no real number line and number ring. They're irrelevant. >>>>> >>>>> ~v~~ >>>> Oh. What causes them? >>> Constant linear velocity in combination with transverse acceleration. >>> >>> ~v~~ >> Constant transverse acceleration? > > What did I say, Tony? Constant linear velocity in combination with > transverse acceleration? Or constant transverse acceleration? I mean > my reply is right there above yours. > > ~v~~ If the transverse acceleration varies, then you do not have a circle. 01oo
From: Tony Orlow on 12 Apr 2007 14:16 Lester Zick wrote: > On 31 Mar 2007 16:56:16 -0700, "Mike Kelly" > <mikekellyuk(a)googlemail.com> wrote: > >> On 1 Apr, 00:36, Tony Orlow <t...(a)lightlink.com> wrote: >>> Lester Zick wrote: >>>> On Fri, 30 Mar 2007 12:10:12 -0500, Tony Orlow <t...(a)lightlink.com> >>>> wrote: >>>>> Lester Zick wrote: >>>>>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <t...(a)lightlink.com> >>>>>> wrote: >>>>>>>>> Their size is finite for any finite number of subdivisions. >>>>>>>> And it continues to be finite for any infinite number of subdivisions >>>>>>>> as well.The finitude of subdivisions isn't related to their number but >>>>>>>> to the mechanical nature of bisective subdivision. >>>>>>> Only to a Zenoite. Once you have unmeasurable subintervals, you have >>>>>>> bisected a finite segment an unmeasurable number of times. >>>>>> Unmeasurable subintervals? Unmeasured subintervals perhaps. But not >>>>>> unmeasurable subintervals. >>>>>> ~v~~ >>>>> Unmeasurable in the sense that they are nonzero but less than finite. >>>> Then you'll have to explain how the trick is done unless what you're >>>> really trying to say is dr instead of points resulting from bisection. >>>> I still don't see any explanation for something "nonzero but less than >>>> finite". What is it you imagine lies between bisection and zero and >>>> how is it supposed to happen? So far you've only said 1/00 but that's >>>> just another way of making the same assertion in circular terms since >>>> you don't explain what 00 is except through reference to 00*0=1. >>>> ~v~~ >>> But, I do. >>> >>> I provide proof that there exists a count, a number, which is greater >>> than any finite "countable" number, for between any x and y, such that >>> x<y, exists a z such that x<z and z<y. No finite number of intermediate >>> points exhausts the points within [x,z], no finite number of >>> subdivisions. So, in that interval lie a number of points greater than >>> any finite number. Call |R in (0,1]| "Big'Un" or oo., and move on to the >>> next conclusion....each occupies how m,uch of that interval? >>> >>> 01oo >> So.. you (correctly) note that there are not a finite "number" of >> reals in [0,1]. You think this "proves" that there exists an infinite >> "number". Why? (And, what is your definition of "number")? > > And what is your definition of "infinite"? > > ~v~~ "greater than any finite" 01oo
From: Virgil on 12 Apr 2007 14:22
In article <461e7764(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Lester Zick wrote: > > And what is your definition of "infinite"? > > > > ~v~~ > > "greater than any finite" > And is TO's definition of finite "less than infinite"? |