The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Lester Zick on 22 Mar 2007 19:04 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. >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. >Ever consider reading, rather than just making stuff up? No. ~v~~
From: stephen on 22 Mar 2007 19:04 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. Stephen
From: Lester Zick on 22 Mar 2007 19:05 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~~
From: Lester Zick on 22 Mar 2007 19:10 On 22 Mar 2007 09:57:31 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: > What does asserting that do for us? Not much. Probably as much as asserting that so many straight line segments constitute a straight line or that there is a real number line or an undefined number of points make up a line segment or a line is made up of points or tables are made up of beer bottles. Six of one, half dozen of the other. Or more likely none of both. ~v~~
From: Lester Zick on 22 Mar 2007 19:11
On Thu, 22 Mar 2007 17:31:19 +0000 (UTC), stephen(a)nomail.com wrote: >In sci.math Mike Kelly <mikekellyuk(a)googlemail.com> wrote: >> On 22 Mar, 16:38, Tony Orlow <t...(a)lightlink.com> wrote: >>> Mike Kelly wrote: >>> >>> > Firstly, the continuum hypothesis is nothing to do with geometry. >>> >>> It does, if sets are combined with measure and a geometrical >>> representation of the question considered. Is half an infinity less than >>> itself? Geometrically, yes, the reals in (0,1] are half the reals in (0,2]. > >> Everything you just said has nothing to do with the continuum >> hypothesis. You're terminally confused. > >> As near as I can tell, your mish-mash of ideas all basically boil down >> to asserting "the 'number' of reals/points in an interval/line segment >> = the Lebesgue measure". What does asserting that do for us? Not much. > >>> > Secondly, division is not defined for infinite cardinal numbers. >>> >>> I'm not interested in cardinality, but a richer system of infinities, >>> thanks. > >> You brought up the continuum hypothesis. Next post, you say you don't >> want to talk about cardinality. Risible. > >Tony thinks that the continuum hypothesis is independent >of cardinality, and that he can just plug in his own notions of "size". >That is about as stupid as thinking that > sqrt(3)^4+sqrt(4)^4=sqrt(5)^4 >is a refutation of Fermat's Last Theorem. Fermat's Last Theorem is about as trivial as Stephen's observations. ~v~~ |