The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
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.
From: Lester Zick on 31 Mar 2007 15:11 On Fri, 30 Mar 2007 12:10:12 -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: >> >>>>> 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~~
From: Lester Zick on 31 Mar 2007 15:12
On Fri, 30 Mar 2007 12:11:23 -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: >> >>>> Equal subdivisions. That's what gets us cardinal numbers. >>>> >>> Sure, n iterations of subdivision yield 2^n equal and generally mutually >>> exclusive subintervals. >> >> I don't know what you mean by mutually exclusive subintervals. They're >> equal in size. Only their position differs in relation to one another. >> >> ~v~~ > >Mutually exclusive intervals : intervals which do not share any points. What points? We don't have any points not defined through bisection and those intervals do share the endpoints with consecutive segments. ~v~~ |