The Definition of Points
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From: Lester Zick on 31 Mar 2007 14:53 On Fri, 30 Mar 2007 11:50:10 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>And the only way we can address >> relations between zeroes and in-finites is through L'Hospital's rule >> where derivatives are not zero or in-finite. And all I see you doing >> is sketching a series of rules you imagine are obeyed by some of the >> things you talk about without however integrating them mechanically >> with others of the things you and others talk about. It really doesn't >> matter whether you put them within the interval 0-1 instead of at the >> end of the number line if there are conflicting mechanical properties >> preventing them from lying together on any straight line segment. >> >> ~v~~ > >Well, if you actually paid attention to any of my ideas, you'd see they >are indeed mostly mechanically related to each other, but you don't seem >interested in discussing the possibly useful mechanics employed therein. Only because you don't seem interested in discussing the mechanics on which the possibly useful mechanics employed therein are based, Tony. I'm less interested in discussing one "possibly useful mechanics" over another when there is no demonstrable mechanical basis for the "possibly useful mechanics" to begin with. You claim they're "mostly mechanically" related but not the mechanics through which they're "mostly mechanically related" except various ambiguous claims per say. ~v~~
From: Virgil on 31 Mar 2007 14:54 In article <460e56a5(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > But all other mathematical objects are equally fantastic, having no > > physical reality, but existing only in the imagination. So any statement > > of mathematical existence is always relative to something like a system > > of axioms. > > Sure, but the question is whether any such assumption of existence > introduces nonsense into your system. It has in each of TO's suggested systems so far. > With the very basic assumption > that subtracting a positive amount from anything makes it less That presumes at least a definition of "positive" and a definition of "amount" and a definition of "subtraction" and a definition of "less" before it makes any sense at all.
From: Lester Zick on 31 Mar 2007 14:55 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~~
From: Virgil on 31 Mar 2007 15:00 In article <460e571f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 30 Mar, 18:25, Tony Orlow <t...(a)lightlink.com> wrote: > ~v~~ > >> An actually infinite sequence is one where there exist two elements, one > >> of which is an infinite number of elements beyond the other. > >> > >> 01oo > > > > Under what definition of sequence? > > > > -- > > mike. > > > > A set where each element has a well defined unique successor within the > set. Good enough? No! if we define the successor of x as x + 1, as we do for the ntaurals, then the set of rationals and the set of reals, with their usual arithmetic, both satisfy your definition of sequence. A sequence should at least be well ordered and have only one member, its first, without a predecessor.
From: Lester Zick on 31 Mar 2007 15:02
On Fri, 30 Mar 2007 12:07:44 -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: >> >>>>> Those aren't geometrical expressions of addition, but iterative >>>>> operations expressed linguistically. >>>> Which means what exactly, that they aren't arithmetic axioms forming >>>> the foundation of modern math? The whole problem is that they don't >>>> produce straight lines or colinear straight line segments as claimed. >> >>> Uh, yeah, 'cause they're not expressed gemoetrically. >> >> Well yes. However until you can show geometric expression are point >> discontinuous I don't see much chance geometric expression will help >> your case any. >> >> ~v~~ > >What does point discontinuity in geometry have to do with anything I've >said? You talk about lines as if they were made up of points. ~v~~ |