The Definition of Points
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From: Lester Zick on 24 Mar 2007 18:42 On 24 Mar 2007 11:43:23 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 23, 6:01 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On 23 Mar 2007 12:33:46 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: >> >> >> >> >On Mar 22, 6:04 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFam...(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 >> >> >Absolutely. And who would you propose teach it? >> >> Moi? > >See below. > >> >> > Do you have any truth >> >to teach? If so, pray tell, where is it? >> >> Wherever. Pray tell when you learn to pay attention in class instead >> of just running your mouth. > >Gladly, just as you as you bring forth the truth you say you are >teaching. Where is it? Well you know you really need to pay attention in class, Draper. >> >> unless of >> >> course you wish to maintain that division by zero is defined even in >> >> neomethematics. >> >> >Did I say that? >> >> What difference does that make/ It makes for good reading especially >> when replying to the posts of others. > >Ah. It's all about the dance, isn't it, Lester. Screw the truth. >You've got dancing to do. Your sentiments exactly. You ask questions. I answer questions. What is it you're afraid of? Or more to the point what is it that you're not afraid of? >> > And how is this related to the statement that an >> >uncountable bunch of zeroes can have nonzero measure? >> >> Beats me. I was hoping you might not be paying attention. > >That clearly is what you hope happens most of the time you post. You >apparently only talk to hear yourself do it. Not much else to do when I'm right and you're not. Which experiment does your family propose exactly? >> You rarely >> do particularly when a reply is addressed to you. > >There you go again, Lester, making the conclusion that a problem on >your end is instead the result of someone else's choices. Which problem on my end did you have in mind exactly? >> Clearly you imagine >> uncountable bunches of zeroes can have nonzero measure. But then >> imagination is what you make of it. >> >> >> >Ever consider reading, rather than just making stuff up? >> >> >> No. >> >> >Ah, well, there's THAT approach, I suppose. >> >> Sauce for the goose I suppose. > >A goose you are, then, by self-proclamation. Yadayada whatever. Ask a stupid question you get a stupid answer. You got a stupid answer to your stupid question. Talk is frugal and you're cheap. ~v~~
From: Lester Zick on 24 Mar 2007 18:44 On Sat, 24 Mar 2007 12:51:51 -0600, Virgil <virgil(a)comcast.net> wrote: >The only proper response to a Zick posting is killfiling him. Sticks and stones . . . etc. Virgil is afraid of nothing except his own shadow. ~v~~
From: RLG on 24 Mar 2007 20:40 "Tony Orlow" <tony(a)lightlink.com> wrote in message news:460520e5(a)news2.lightlink.com... > > 1=0.999...? 1 = 0.999... Multiply both sides of this equation by 10 to get: 10 = 9.999... Substract the original equation from this one to get: 9 = 9. So 0.999... is simply another way of writing the number 1. If you don't like that then write 0.999... as follows: 9*( 1/10 + 1/100 + 1/1000 + ...) Notice that we have an infinite geometric series with x=1/10: x + x^2 + x^3 + x^4 + ... = x/(1-x) This gives us (1/10)/(1-(1/10)) = 1/9 which gives us: 9*( 1/10 + 1/100 + 1/1000 + ...) = 9*(1/9) = 1 R
From: The Ghost In The Machine on 24 Mar 2007 20:44 In sci.physics, RLG <Junk(a)Goldolfo.com> wrote on Sat, 24 Mar 2007 16:40:04 -0800 <nM6dnRdlcfJKK5jbnZ2dnUVZ_rWnnZ2d(a)comcast.com>: > > "Tony Orlow" <tony(a)lightlink.com> wrote in message > news:460520e5(a)news2.lightlink.com... >> >> 1=0.999...? > > > 1 = 0.999... > > Multiply both sides of this equation by 10 to get: > > 10 = 9.999... > > Substract the original equation from this one to get: > > 9 = 9. A little more complicated than that, as one could either use that logic, resulting in 9.0000..., or assume an infinite borrow, resulting in 8.9999... . The proper method of handling this would be using limits, which you implicitly do below: > > So 0.999... is simply another way of writing the number 1. If you don't > like that then write 0.999... as follows: > > 9*( 1/10 + 1/100 + 1/1000 + ...) > > Notice that we have an infinite geometric series with x=1/10: > > x + x^2 + x^3 + x^4 + ... = x/(1-x) > > This gives us (1/10)/(1-(1/10)) = 1/9 which gives us: > > 9*( 1/10 + 1/100 + 1/1000 + ...) = 9*(1/9) = 1 A geometric series of n terms results in a * (1 - r^(n+1))/(1-r); if -1 < r < 1, lim(n->+oo) r^(n+1) will be 0. It's a bit like Zeno's paradox, which one can write 1/2 + 1/4 + 1/8 + ... Zeno argued this was infinite and that motion was impossible (obviously his logic was a little off, since in order to speak or write one has to move something); modern math would simply write this as 1 = 1/2 + 1/4 + 1/8 + ... for reasons similar to 0.999... = 1. In fact, 0.111...(2) = 1, in binary. > > > R > > -- #191, ewill3(a)earthlink.net -- insert random pedancy here Useless C++ Programming Idea #104392: for(int i = 0; i < 1000000; i++) sleep(0); -- Posted via a free Usenet account from http://www.teranews.com
From: RLG on 24 Mar 2007 22:59
"The Ghost In The Machine" <ewill(a)sirius.tg00suus7038.net> wrote in message news:v8tgd4-1qv.ln1(a)sirius.tg00suus7038.net... > In sci.physics, RLG > <Junk(a)Goldolfo.com> > wrote > on Sat, 24 Mar 2007 16:40:04 -0800 > <nM6dnRdlcfJKK5jbnZ2dnUVZ_rWnnZ2d(a)comcast.com>: >> >> "Tony Orlow" <tony(a)lightlink.com> wrote in message >> news:460520e5(a)news2.lightlink.com... >>> >>> 1=0.999...? >> >> >> 1 = 0.999... >> >> Multiply both sides of this equation by 10 to get: >> >> 10 = 9.999... >> >> Substract the original equation from this one to get: >> >> 9 = 9. > > A little more complicated than that, as one could either use that logic, > resulting in 9.0000..., or assume an infinite borrow, resulting in > 8.9999... . The proper method of handling this would be using limits, > which you implicitly do below: Just curious, how would an infinite borrow be done? The method I used had 10-1=9 and: 9.99999... 0.99999... ----------- 9.00000... R |