The Definition of Points
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From: Bob Kolker on 31 Mar 2007 16:13 Lester Zick wrote: > > > You talk about lines as if they were made up of points. In one model of Euclidean geometry that satisfies all of Hilbert's Axioms the lines are made up of points. Furthermore it can be shown Hilbert's Axioms are categorical, so all models are isometric. So a line is made up of points in -any- model for Hilbert's Axioms. Bob Kolker
From: Bob Kolker on 31 Mar 2007 16:14 Virgil wrote: > > 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. A stopped clock? Except Zick is not riight twice a day. Possibly twice a year though. Bob Kolker
From: Bob Kolker on 31 Mar 2007 16:18 Lester Zick wrote: > > Mathematikers still can't say what an infinity is, Bob, and when they > try to they're just guessing anyway. So I suppose if we were to take > your claim literally we would just have to conclude that what made > physics possible was guessing and not mathematics at all. Not true. Transfite cardinality is well defined. In projective geometry points at infinity are well defined (use homogeneous coordinates). You are batting 0 for n, as usual. Bob Kolker
From: stephen on 31 Mar 2007 16:54 In sci.math Brian Chandler <imaginatorium(a)despammed.com> wrote: > stephen(a)nomail.com wrote: >> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> > If all other elements in the sequence are a finite number >> > of steps from the start, and w occurs directly after those, then it is >> > one step beyond some step which is finite, and so is at a finite step. >> >> So you think there are only a finite number of elements between 1 and >> w? What is that finite number? 100? 100000? 100000000000000000? >> 98042934810235712394872394712349123749123471923479? Which one? > None of the ones you've mentioned. Although it is, of course, a > perfectly ordinary natural number, in that one can add 1 to it, or > divide it by 2, its value is Elusive. Only Tony could actually write > it down. These Elusive numbers have amazing properties. According to Tony, there are only a finite number of finite naturals. There exists some finite natural Q such that the set { 1,2,3,4,.... Q} is the set of all finite natural numbers. But what of Q+1? Well we have a couple of options: a) Q+1 does not exist b) Q+1 is not a finite natural number c) { 1,2,3,4, ... Q} is not the set of all finite natural numbers Tony rejects all these options, and apparently has some fourth Elusive option. Stephen
From: Tony Orlow on 31 Mar 2007 18:09
Bob Kolker wrote: > Tony Orlow wrote: >> >> As I said to Brian, it's provably the size of the set of finite >> natural numbers greater than or equal to 1. No, there is no last >> finite natural, and no, there is no "size" for N. Aleph_0 is a phantom. > > No. It is the cardinality of the set of integers. No, Bob, that's a Muslim lie, perpetrated by the Jews as a joke on the xtians. > > Deep in your heart you want everything to be finite. That will limit > mathematics to totally up grocery bills and such like. No, Bob, life is not simply a marketplace for me, as it is for you. > > Mathematics based on infinities has made physics possible. > Measure makes physics possible. > Bob Kolker Tony Orlow. |