The Definition of Points
in [Math]
|
Prev: Guide to presenting Lemma, Theorems and Definitions
Next: Density of the set of all zeroes of a function with givenproperties
From: Tony Orlow on 31 Mar 2007 19:58 stephen(a)nomail.com wrote: > In sci.math Brian Chandler <imaginatorium(a)despammed.com> wrote: >> stephen(a)nomail.com wrote: >>> In sci.math Tony Orlow <tony(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... Tony
From: Tony Orlow on 31 Mar 2007 20:01 Bob Kolker wrote: > Tony Orlow wrote:>> >> >> Measure makes physics possible. > > On compact sets which must have infinite cardinality. > > The measure of a dense countable set is zero. > > Bob Kolker Yes, some finite multiple of an infinitesimal. Tony Orlow
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 |