The Definition of Points
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From: Lester Zick on 22 Mar 2007 13:08 On 22 Mar 2007 03:32:12 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >Saying "the number of points in an interval is oo * the length of the >interval" doesn't add anything to geometry. Sorry. Doesn't add anything to SOAP operas either. ~v~~
From: Lester Zick on 22 Mar 2007 13:24 On Wed, 21 Mar 2007 22:45:54 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Wed, 21 Mar 2007 14:17:16 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> It states the specific infinite number of points in the unit interval, >>> say, on the real line. >> >> And what real line would that be, Tony? >> >> ~v~~ > >The one that fully describes the real numbers. You mean a straight line that describes curves exactly? Or some curve that describes straight lines exactly? > Like, duh! The one that >exists. Except there is no such line, Tony. At least none that describes both curves and straight lines together exactly.And if you don't believe me Bob Kolker has acknowledged the point previously. >E R >0eR >1eR >0<1 >xeR ^ yeR ^ x<y -> EzeR x<z ^ z<y Very fanciful, Tony. You mean if you know the approximation for pi lies between 3 and 4 on a straight line pi itself does too? You see, Tony, this is the basic reason I refuse to be drawn into discussion on collateral mathematical issues as interesting as they might be. I can't even get the most elementary point across even to those supposedly paying attention to what I say. ~v~~
From: Lester Zick on 22 Mar 2007 13:27 On 21 Mar 2007 12:32:13 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >Don't waste time responding to me. I have no interest in conversing >with trolls, no matter how clever or amusing they think themselves. Apparently you have no interest in truth either. ~v~~
From: Lester Zick on 22 Mar 2007 13:28 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~~
From: stephen on 22 Mar 2007 13:31
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. Stephen |