The Definition of Points
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From: Lester Zick on 23 Mar 2007 12:50 On Thu, 22 Mar 2007 20:14:43 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >> >>> On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >>>> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> >>>> wrote: >> >> >>>>> Lester Zick wrote: >>>>>> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowh...(a)nowhere.com> >>>>>> wrote: >>>>>>> Tony Orlow wrote: >>>>>>>> There is no correlation between length and number of points, because >>>>>>>> there is no workable infinite or infinitesimal units. Allow oo points >>>>>>>> per unit length, oo^2 per square unit area, etc, in line with the >>>>>>>> calculus. Nuthin' big. Jes' give points a size. :) >>>>>>> Points (taken individually or in countable bunches) have measure zero. >>>>>> They probably also have zero measure in uncountable bunches, Bob. At >>>>>> least I never heard that division by zero was defined mathematically >>>>>> even in modern math per say. >>>>>> ~v~~ >>>>> Purrrrr....say! Division by zero is not undefinable. One just has to >>>>> define zero as a unit, eh? >>>> A unit of what, Tony? >>>> >>>>> Uncountable bunches certainly can attain nonzero measure. :) >>>> Uncountable bunches of zeroes are still zero, Tony. >>>> >>> Why no, no they're not, Lester. >> >> Of course you say so, Draper. Fact is that uncountable bunches of >> infinitesimals are not zero but non uncountable bunches of zeroes are. >> > >"zero" and "infinitesimal" are often used interchangeably, Not by mathematicians they're not. That's why you can have a zero and 0 dr. Huge difference. > but they >really mean slightly different things, as I learned early on here. Definitely not from mathematikers. They spend all their time talking about arithmetic and arithmetic SOAP "models". >>> Perhaps a course in real analysis would be of value. >> >> And perhaps a course in truth would be of value to you unless of >> course you wish to maintain that division by zero is defined even in >> neomethematics. >> > >It should be, on each level of relatively infinite scale... On a infinitesimal scale perhaps. Not on a scale on zero. There is no scale on zero. That's exactly why division by zero is not defined even in neomathematics. Contrary to the fond hopes and desires of those looking to integrate points into lines. Yeah. Good luck with that one. >>> Ever consider reading, rather than just making stuff up? >> >> No. ~v~~
From: Lester Zick on 23 Mar 2007 12:53 On Thu, 22 Mar 2007 20:15:37 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 22 Mar 2007 17:15:35 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowhere(a)nowhere.com> >>>>>> wrote: >>>>>> >>>>>>> Tony Orlow wrote: >>>>>>>> There is no correlation between length and number of points, because >>>>>>>> there is no workable infinite or infinitesimal units. Allow oo points >>>>>>>> per unit length, oo^2 per square unit area, etc, in line with the >>>>>>>> calculus. Nuthin' big. Jes' give points a size. :) >>>>>>> Points (taken individually or in countable bunches) have measure zero. >>>>>> They probably also have zero measure in uncountable bunches, Bob. At >>>>>> least I never heard that division by zero was defined mathematically >>>>>> even in modern math per say. >>>>>> >>>>>> ~v~~ >>>>> Purrrrr....say! Division by zero is not undefinable. One just has to >>>>> define zero as a unit, eh? >>>> A unit of what, Tony? >>>> >>>>> Uncountable bunches certainly can attain nonzero measure. :) >>>> Uncountable bunches of zeroes are still zero, Tony. >>>> >>>> ~v~~ >>> Infinitesimal units can be added such that an infinite number of them >>> attain finite sums. >> >> And since when exactly, Tony, do infinitesimals equal zero pray tell? >> >> ~v~~ > >Only in the "standard" universe, Lester. So 1-1="infinitesimal" Tony? Somehow I doubt that's exactly what Newton and Leibniz had in mind with their calculus. ~v~~
From: Lester Zick on 23 Mar 2007 12:53 On Thu, 22 Mar 2007 23:04:51 +0000 (UTC), stephen(a)nomail.com wrote: >In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> Mike Kelly wrote: >>> >>> You brought up the continuum hypothesis. Next post, you say you don't >>> want to talk about cardinality. Risible. > >> CH is a question in ZFC. The answer lies outside ZFC. > >Just like the answer to Fermat's Last Theorem lies outside >the integers. You mean there's something SOAP operas can't model? ~v~~
From: Lester Zick on 23 Mar 2007 12:54 On 22 Mar 2007 16:38:00 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >> CH is a question in ZFC. The answer lies outside ZFC. > >Risible. So are SOAP operas. ~v~~
From: Lester Zick on 23 Mar 2007 12:56
On 23 Mar 2007 01:10:58 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >This was supposed to be about you stating what the "limitations" of >the current axiomatisation of geometry are. You haven't done so. So what are the limitations of SOAP operas? None that I've heard of. ~v~~ |