The Definition of Points
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From: Lester Zick on 31 Mar 2007 20:02 On 31 Mar 2007 10:05:47 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: >Tony Orlow wrote: >> Mike Kelly wrote: >> > On 31 Mar, 13:41, Tony Orlow <t...(a)lightlink.com> wrote: >> >> Mike Kelly wrote: >> >>> On 30 Mar, 18:25, Tony Orlow <t...(a)lightlink.com> wrote: >> >>>> Lester Zick wrote: > ><oh grief, I expect he did> Of course he did. >> >>> Under what definition of sequence? > >> >> A set where each element has a well defined unique successor within the >> >> set. > >> > So any set is a sequence? For any set, take the successor of each >> > element as itself. > >> There is no successor in a pure set. That only occurs in a discrete >> linear order. > >Unlike Lester, I think you really do have enough brains to understand >simple mathematics if you tried. Most simpletons do. You, Mike, Stephen, Virgil, et al. come to mind. > Why oh why do you not read a book, so >you wouldn't need to spew out confused babble like the above. (Pure >poetry though it may be in your own private language.) As opposed to your private language? ~v~~
From: Lester Zick on 31 Mar 2007 20:03 On Fri, 30 Mar 2007 12:27:40 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>> Just ask yourself, Tony, at what magic point do intervals become >>>> infinitesimal instead of finite? Your answer should be magnitudes >>>> become infintesimal when subdivision becomes infinite. >>> Yes. >> >> Yes but that doesn't happen until intervals actually become zero. >> >>> But the term >>>> "infinite" just means undefined and in point of fact doesn't become >>>> infinite until intervals become zero in magnitude. But that never >>>> happens. >>> But, but, but. No, "infinite" means "greater than any finite number" and >>> infinitesimal means "less than any finite number", where "less" means >>> "closer to 0" and "more" means "farther from 0". >> >> Problem is you can't say when that is in terms of infinite bisection. >> >> ~v~~ > >Cantorians try with their lame "aleph_0". Better you get used to the >fact that there is no more a smallest infinity than a smallest finite, >largest finite, or smallest or largest infinitesimal. Those things >simply don't exist, except as phantoms. Does anyone really care? ~v~~
From: Tony Orlow on 31 Mar 2007 20:06 Virgil wrote: > In article <460edc26(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Bob Kolker wrote: >>> Tony Orlow wrote: >>>> As I said to Brian, it's provably the size of the set of finite >>>> natural numbers greater than or equal to 1. No, there is no last >>>> finite natural, and no, there is no "size" for N. Aleph_0 is a phantom. >>> No. It is the cardinality of the set of integers. >> No, Bob, that's a Muslim lie, perpetrated by the Jews as a joke on the >> xtians. > > And does TO pretend to have a mathematically valid proof of that claim? Allah: I am the last prophet. Jehovah: My last prophet is second only to me. El: There is none close to Us. Jesus: Come sit next to me. Therefore, according to obviously plain logic, I'm right, of course! QED. Tony
From: Lester Zick on 31 Mar 2007 20:06 On Fri, 30 Mar 2007 12:31:08 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <460d489b(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Lester Zick wrote: >> > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> > wrote: >> > >> >>> Just ask yourself, Tony, at what magic point do intervals become >> >>> infinitesimal instead of finite? Your answer should be magnitudes >> >>> become infintesimal when subdivision becomes infinite. >> >> Yes. >> > >> > Yes but that doesn't happen until intervals actually become zero. >> > >> >> But the term >> >>> "infinite" just means undefined and in point of fact doesn't become >> >>> infinite until intervals become zero in magnitude. But that never >> >>> happens. >> >> But, but, but. No, "infinite" means "greater than any finite number" and >> >> infinitesimal means "less than any finite number", where "less" means >> >> "closer to 0" and "more" means "farther from 0". >> > >> > Problem is you can't say when that is in terms of infinite bisection. >> > >> > ~v~~ >> >> Cantorians try with their lame "aleph_0". Better you get used to the >> fact that there is no more a smallest infinity than a smallest finite, >> largest finite, or smallest or largest infinitesimal. Those things >> simply don't exist, except as phantoms. > >But all other mathematical objects are equally fantastic, having no >physical reality, but existing only in the imagination. So any statement >of mathematical existence is always relative to something like a system >of axioms. Whew. Means you don't have to consider whether they're true. Quite a relief I'd say. You can always take it up with someone who unlike yourself isn't too lazy or stupid to think for a living. ~v~~
From: Mike Kelly on 31 Mar 2007 20:06
On 1 Apr, 00:58, Tony Orlow <t...(a)lightlink.com> wrote: > step...(a)nomail.com wrote: > > In sci.math Brian Chandler <imaginator...(a)despammed.com> wrote: > >> step...(a)nomail.com wrote: > >>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>> If all other elements in the sequence are a finite number > >>>> of steps from the start, and w occurs directly after those, then it is > >>>> one step beyond some step which is finite, and so is at a finite step. > >>> So you think there are only a finite number of elements between 1 and > >>> w? What is that finite number? 100? 100000? 100000000000000000? > >>> 98042934810235712394872394712349123749123471923479? Which one? > > >> None of the ones you've mentioned. Although it is, of course, a > >> perfectly ordinary natural number, in that one can add 1 to it, or > >> divide it by 2, its value is Elusive. Only Tony could actually write > >> it down. > > > These Elusive numbers have amazing properties. According to > > Tony, there are only a finite number of finite naturals. > > There exists some finite natural Q such that the set > > { 1,2,3,4,.... Q} > > is the set of all finite natural numbers. But what of Q+1? > > Well we have a couple of options: > > a) Q+1 does not exist > > b) Q+1 is not a finite natural number > > c) { 1,2,3,4, ... Q} is not the set of all finite natural numbers > > > Tony rejects all these options, and apparently has some fourth > > Elusive option. > > > Stephen > > Oy. The "elusive" option is that there is no acceptable "size" for N. > That was really hard to figure out after all this time... Lucky, then, that set theory don't refer to the "size" of sets but rather to their "cardinality". You still haven't figured that out after all this time. It's a very strange mental block to have. -- mike. |