The Definition of Points
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From: Lester Zick on 14 Apr 2007 15:20 On 13 Apr 2007 11:36:03 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >> I've discussed that with you and others. It doesn't cover the cases I am >> talking about. The naturals have a "measure" of 0, no? So, measure >> theory doesn't address the relationship between, say, the naturals and >> the evens or primes. It's not as general as it should be. So, what do >> you want me to say? > >Nothing, really, until you learn the mathematics you're pretending to >know about. Whereas you yourself should say whatever you want, Moe(x), about the mathematics you're pretending to know about? What mathematics would that be anyway, SOAP operas? ~v~~
From: Lester Zick on 14 Apr 2007 15:26 You know, Moe(x), I've never read quite the collection of buzzwords you provide here in any one location before. Is mathematics to you just a set of all slogans in any given domain of discourse? On 13 Apr 2007 14:32:45 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >On Apr 13, 12:51 pm, Tony Orlow <t...(a)lightlink.com> wrote: >> MoeBlee wrote: >> > On Apr 13, 11:25 am, Tony Orlow <t...(a)lightlink.com> wrote: >> >> >> I've discussed that with you and others. It doesn't cover the cases I am >> >> talking about. The naturals have a "measure" of 0, no? So, measure >> >> theory doesn't address the relationship between, say, the naturals and >> >> the evens or primes. It's not as general as it should be. So, what do >> >> you want me to say? >> >> > Nothing, really, until you learn the mathematics you're pretending to >> > know about. >> >> I didn't bring up "measure theory". > >Where do I begin: transitivity, ordering, recursion, axiom of >infinity, non-standard analysis...on and on and on... > >> > Nothing to which you responded "pretends" that cardinality "can tell >> > things it can't". What SPECIFIC theorem of set theory do you feel is a >> > pretense of "telling things that it can't"? >> >> AC > >If you mean non-constructivity, then no one disputes that the axiom of >choice is non-constructive. No one says that the axiom of choice >proves the existence of a definable well ordering. > >But if you require constructivity then you can't without contradiction >endorse Robinson's non-standard analysis. > >> >>> It has CARDINALITY aleph_0. If you take "size" to mean cardinality >> >>> then aleph_0 is the "size" of the set of naturals. But it simply isn't >> >>> true that "a set of naturals with 'size' y has maximum element y" if >> >>> "size" means cardinality. >> >> I don't believe cardinality equates to "size" in the infinite case. >> >> > Wow, that is about as BLATANTLY missing the point of what you are in >> > immediate response to as I can imagine even you pulling off. >> >> > MoeBlee >> >> What point did I miss? > >The MAJOR point - the hypothetical nature of mathematical reasoning >(think about the word 'if' twice in the poster's paragraph) and the >inessentiality of what words we use to name mathematical objects and >their properties. > >I've been trying to get you to understand that for about two years >now. > >> I don't take transfinite cardinality to mean >> "size". You say I missed the point. You didn't intersect the line. > >You just did it AGAIN. We and the poster to whom you responded KNOW >that you don't take cardinality as capturing your notion of size. The >point is then just for your to recognize that IF by 'size' we mean >cardinality, then certain sentences follow and certain sentences don't >follow and that what is important is not whether we use 'size' or >'cardinality' or whatever word but rather the mathematical relations >that are studied even if we were to use the words 'schmize' or >'shmardinal' or whatever. > >MoeBlee > ~v~~
From: Lester Zick on 14 Apr 2007 15:30 On 14 Apr 2007 04:20:31 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >>I'm not the only one in the revolution against blind axiomatics. > >Blind axiomatics? So you think ZFC was developed by blindly? People >picked the axioms randomly without any real consideration for what the >consequences would be? Please. ZF(C) provides a foundation for >virtually all modern mathematics. This didn't happen by accident. Sure it did. Someone decided they wanted SOAP operas instead of mathematics and the rest is history. >What's "blind" about ZF(C)? What great insight do you think is missed >that you are going to provide, oh mighty revolutionary? What >mathematics can be done with your non-existant foundation that can't >be done in ZF(C)? Spelling apparently. ~v~~
From: Virgil on 14 Apr 2007 15:39 In article <462117d1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > Blind axiomatics? So you think ZFC was developed by blindly? People > > picked the axioms randomly without any real consideration for what the > > consequences would be? Please. ZF(C) provides a foundation for > > virtually all modern mathematics. This didn't happen by accident. > > > > What's "blind" about ZF(C)? What great insight do you think is missed > > that you are going to provide, oh mighty revolutionary? What > > mathematics can be done with your non-existant foundation that can't > > be done in ZF(C)? > > > > Axiomatically, I think the bulk of the burden lies on Choice in its full > form. Dependent or Countable Choice seem reasonable, but a blanket > statement for all sets seems unjustified. Since it has been shown that if ZF is consistent then ZFC must be consistent as well, what part of ZF does TO object to? > >> Then how do you presume to declare that my statement is "not true"? > >> > > No answer? Do you retract the claim? > > >>> It's very easily provable that if "size" means "cardinality" that N > >>> has "size" aleph_0 but no largest element. You aren't actually > >>> questioning this, are you? > >> No, have your system of cardinality, but don't pretend it can tell > >> things it can't. Cardinality is size for finite sets. For infinite sets > >> it's only some broad classification. It is one form of size for all sets. One might use the physical analogy that volume, surface area, and maximum linear dimension are all measures of the size of a solid. So implying that one "size" fits all is false. > > OK so all of the above comes down to you demanding that we don't call > > cardinality "size". If we don't call cardinality "size" then all your > > objections to cardinality disappear. > > It would also be nice to have an alternative to cardinality Why? > > So, what's your opinion of infinite-case induction, IFR and N=S^L, and > multilevel logics, again? I forget. AS presented by TO, garbage, garage and garbage. There is a transfinite induction but it doesn't work the way TO would have it work, and there are a wide variety of logics none of which seems to work at all like TO would have them work.
From: Lester Zick on 14 Apr 2007 15:42
On 14 Apr 2007 04:20:31 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >> > Here's a hint, Tony : Ross and Lester are trolls. They don't beleive a >> > damn word they say. Naturally I don't have to believe a word I say when I can and do prove every word I say whereas mathematikers are required to believe every word they say and find faith essential because they can't. > They are jerks getting pleasure from intentionally >> > talking rubbish to solicit negative responses. Responding to them at >> > all is pointless. Responding to them as though their "ideas" are >> > serious and worthy of attention makes you look very, very silly. >> >> Yes, it's very silly to entertain fools, except when they are telling >> you the Earth is round. One needn't be all like that, Mike. When you >> argue with a fool, chances are he's doing the same. > >Nope. Ross and Lester are trolls. They are laughing at you when you >agree with their fake online personas. Continue wasting your time on >them if you like. I don't take Tony to be quite the fool I take you to be, Mike. At least Tony's capable of judging issues you prefer to avoid with hostility and vituperation so characteristic of those who prefer to judge people instead of issues. I've always found it interesting mathematikers convert so readily from numbers to psychology the moment their word count exceeds that of primitive people, you know "one, two, three, . . . many". ~v~~ |