The Definition of Points
in [Math]
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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~~
From: Lester Zick on 31 Mar 2007 15:04 On Fri, 30 Mar 2007 12:08:06 -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: >> >>>>> So, start with the straight line: >>>> How? By assumption? As far as I know the only way to produce straight >>>> lines is through Newton's method of drawing tangents to curves. That >>>> means we start with curves and derivatives not straight lines.And that >>>> means we start with curved surfaces and intersections between them. >>>> >>> Take long string and tie to two sticks, tight. >> >> Which doesn't produce straight line segments. >> >> ~v~~ > >Yeah huh Yeah indeed. ~v~~
From: Virgil on 31 Mar 2007 15:05 In article <460e5899$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > It is not even true in Tony's mathematics, at least it was not true > > the last time he brought it up. According to this > > definition {1, 2, 3, ... } is not actually infinite, but > > {1, 2, 3, ..., w} is actually infinite. However, the last time this > > was pointed out, Tony claimed that {1, 2, 3, ..., w} was not > > actually infinite. > > > > Stephen > > No, adding one extra element to a countable set doesn't make it > uncountable. Countability is a straw man. The issue is whether adding one element converts a "not actually infinite" set into an "actually infinite" set.
From: Virgil on 31 Mar 2007 15:09
In article <460e812f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Surely, you don't think me fool enough to think that Virgil would > actually give me a sincere compliment, or acknowledge that any of my > nonstandard points actually has any merit, do you? Still, it was nice of > Virgil to say I'm not worst ignoramus he knows. That warmed my heart. > > Still, I don't know what Virgil's comment about me says about my future > responses to you. See above for a characterization of Q. I have, upon occasion, found, and stated, that TO was correct on some point or another. I have never found Zick to be correct on any point. But then I have long since stopped looking at Zick's posts. I suppose that it is marginally possible that Zick may have been right about something since then. |