An uncountable countable set
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From: Tony Orlow on 27 Sep 2006 11:04 Randy Poe wrote: > Tony Orlow wrote: >> Randy Poe wrote: >>> Tony Orlow wrote: >>>> Randy Poe wrote: >>>>> Tony Orlow wrote: >>>>>> Virgil wrote: >>>>>>> In article <45189d2a(a)news2.lightlink.com>, >>>>>>> Tony Orlow <tony(a)lightlink.com> wrote: >>>>>>> >>>>>>>> Virgil wrote: >>>>>>>>> In article <45187409(a)news2.lightlink.com>, >>>>>>>>> Tony Orlow <tony(a)lightlink.com> wrote: >>>>>>>> If so, then why do you say "There is no >>>>>>>> infinite case"? >>>>>>> Because there isn't any. >>>>>> There is no noon in the Zeno machine? >>>>> There's no ball put in at noon in the Zeno machine. >>>>> >>>>> All cases, all Zeno balls, are put in before noon. >>>>> >>>>> - Randy >>>>> >>>> At any time finitely before noon, only a finite number of balls have >>>> been processed. Do you disagree? >>> I agree. >>> >>>> Are you suggesting that the vase fills >>>> at some *infinitesimal* amount of time before noon? >>> No. There is no time before noon when the vase is full. >>> Let t be any time before noon. Infinitely many balls >>> will be inserted into the vase after t, but before noon. >>> >>>> How does that differ, in your view, from being *at* noon? >>> Well since I also don't say "it fills at an infinitesimal >>> time before noon", there is no need to distinguish >>> one nonsensical statement from the other. >>> >> But, you do say it fills, > > Probably not. I wouldn't know how to describe "full" > for an infinite vase. > >> or empties, right? > > It definitely empties, since every ball you put in is > later taken out. So, it definitely empties...... > >> And, at the same time you >> say it does not do so at noon, nor does it do so before noon. When does >> this occur? > > It doesn't. ....but it doesn't! Wow, that's deep. Math is cool. > There is no last ball, so I wouldn't say there's > a point where the nonexistent last ball goes in, nor > would I say there's a full state corresponding to the > nonexistent last ball. Oh definitely not. I mean, definitely. Or not. > > So the reason I don't say it's full "an infinitesimal time > before noon" or "some other time before noon" is that > I don't say it's full. But, you do say it's full or empty, right? :| > > - Randy > Tony
From: imaginatorium on 27 Sep 2006 11:59 Tony Orlow wrote: > Randy Poe wrote: > > Tony Orlow wrote: > >> Randy Poe wrote: > >>> Tony Orlow wrote: > >>>> Randy Poe wrote: > >>>>> Tony Orlow wrote: > >>>>>> Virgil wrote: > >>>>>>> Tony Orlow <tony(a)lightlink.com> wrote: .... much, leading nowhere. Tony, Would you care to answer me some questions? No tricks or anything, just something about what we would call graphs in the x-y plane? Here's a starter: Consider a (notional, theoretical, mathematical, not physical) x-y plane. That is, an area in which there is a point (0,0) in some particular place, an x-axis, y-axis, and points are identified by coordinates x and y, using (in normal maths) real values for these coordinates. Consider (for convenience) that this plane is embedded in a notional graphics application, with a "Fill" function. So if we draw the circle x^2 + y^2 = 49 (centre origin, (constant! Zick, be quiet!) radius 7), then click with the Fill function on the point (2,1), it fills the circle, and no paint spills outside that radius 7. Now suppose we have the graphs of x=2 and x=5. Vertical lines, extending up and down without limit. Suppose we click with the Fill function on the point (3, 4), what would you say happens? Obviously paint fills the vertical strip of width 3. Would you say that any paint was able to "spill" around the (nonexistent!) "top" of either of the graphs, and somehow fill more of the plane than this strip, or would you say we just get a (vertically) unbounded strip of blue? (Goddabe blue!) If you care to answer, I'd like to ask one or two more similar questions. If you don't want to bother, please say, and I will save my time. Brian Chandler http://imaginatorium.org
From: Virgil on 27 Sep 2006 15:31 In article <c43c$451a2703$82a1e228$4034(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>Tony Orlow wrote: > >> > >>>Math=Science? > >> > >>Definitely, yes! > > > > Only if science is a subset of mathematics. > > Science is not a subset of mathematics. Neither is mathematics a subset > of science nowadays. If 1 = yes and 0 = no : > > mathematics | science | result > ------------------------------ > 0 0 having a chat > 0 1 soft sciences > 1 0 nonsense maths > 1 1 exact sciences > > Han de Bruijn Correction: mathematics | science | result ---------------------------------------------- 0 0 having a chat 0 1 nonsense sciences 1 0 not yet applied maths 1 1 exact sciences
From: Virgil on 27 Sep 2006 15:34 In article <24699$451a2a4a$82a1e228$6662(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > MoeBlee wrote: > > > Tony Orlow wrote: > > > >>Constructivism and Axiomatism are two sides of a coin. They can be > >>reconciled in larger framework, I think. > > > > I don't know what your definition of 'axiomatism' is, but there are > > axiomatic systems for constructive mathematics. > > True. And I consider that as a distortion of contructivism. The question is whether the foremost of the constructivists do. > > Abandon Axioms and Acquire an Abacus (: Mueckenheim ?) > > Han de Bruijn
From: Virgil on 27 Sep 2006 15:39
In article <451a891f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >> Tony Orlow wrote: > >> > >>> Han de Bruijn wrote: > >>>> I may be rude sometimes, but I never get _personal_ by calling somebody > >>>> an "idiot" or a "crank". Tony's "babbling" translates with Euroglot as > >>>> "babbelen" in Dutch, which is a word I can use here in the conversation > >>>> with my collegues without making them very angry (if I say "volgens mij > >>>> babbel je maar wat"). But, of course, I cannot judge the precise impact > >>>> of the word in English. Apologies if it is heavier than I thought. > >>> Do you have the saying, "Shallow brooks babble, and still waters run > >>> deep"? I figured you picked up the usage from this forum, actually. It's > >>> meant, in English, to mean you aren't making any sense. :) > >> I have talked to my collegues and they have told me that "babbling" in > >> English indeed has a meaning which is somewhat different from "babbelen" > >> in Dutch. It is more like our "lallen", to be translated in English as > >> "talking while you are drunk". Is that correct ? > >> > >> "Babbelen" in Dutch is more like "having a nice chat". It's not that it > >> doesn't make any sense, but it's not very deep either. It's more social > >> than intellectual. > >> > >>> Math=Science? > >> Definitely, yes! > > > > Only if science is a subset of mathematics. > > There is no science without mathematics, if that's what you mean. There are certainly areas of study which call themselves sciences which are at most peripherally mathematical, such as much of psychology. |