An uncountable countable set
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From: Lester Zick on 1 Nov 2006 17:09 On 31 Oct 2006 12:48:24 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: >> On 30 Oct 2006 16:52:02 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >> >> >Tony Orlow wrote: >> >> stephen(a)nomail.com wrote: >> > >> >> > The point is, there are different types of numbers, and statements >> >> > that are true of one type of number need not be true of other >> >> > types of numbers. >> > >> >> Well, then, you must be of the opinion that set theory is NOT the >> >> foundation for all mathematics, but only some particular system of >> >> numbers and ideas: a theory. That's good. >> > >> >Whether he thinks set theory is or is not a foundation, it doesn't >> >follow that he should not think it is a foundation simply because there >> >are different kinds of numbers. >> >> Huh? Maybe you could run that by us again, Moe. > >That there are different kinds of numbers does not entail that set >theory cannot be a foundation. Nor does it entail that set theory can be. ~v~~
From: Lester Zick on 1 Nov 2006 17:11 On 31 Oct 2006 21:06:43 -0800, imaginatorium(a)despammed.com wrote: > >Lester Zick wrote: >> On Tue, 31 Oct 2006 10:30:08 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >> [. . .] >> >> Tony, I'm going to post several replies to this one post because I've >> come up with a couple of ideas which may (or may not) appeal to you. >> >> First off why not change your approach in the following way. It seems >> to me that you could arrange all the naturals on the x axis. Then >> instead of trying to cram in all the transcendentals on the same axis, >> try putting transcendental infinites on the ordinal y axis instead. >> >> However if you try this approach you may find that you need another >> mutually orthogonal z axis to accommodate another class of infinites. >> I don't know if this is going to work completely or not. But I think >> it holds considerably more promise than trying to accommodate it all >> on one more or less circular x axis alone. >> >> In any event this is the end of this particular suggestion. I hope it >> helps and sheds some light on what I think is going on in mechanical >> terms. In any event I'll get back to your original message now plus >> what I think will turn out to be definitive mechanical arguments on >> the subject of transcendentals and conventional linear analysis of the >> reals. >> >> ~v~~ > >Oh Lester - you really are a hoot!! Hoot, hoot. >Out of curiosity, suppose the natural 2 is at (2,0) in conventional x-y >coordinates, and pi (which I believe you agree is transcendental) is at >say (0,7), whereabouts would 2pi be? Somewhere off to the side in zenland, Brian. ~v~~
From: cbrown on 1 Nov 2006 17:17 imaginatorium(a)despammed.com wrote: > Mike Kelly wrote: > > Tony Orlow wrote: > > > Mike Kelly wrote: > > > > Tony Orlow wrote: > > <snip> > > > > > 2) How come noon "exists" in this experiment but it didn't exist in the > > > > original experiment? Or did you give up on claiming noon doesn't > > > > "exist"? What does that mean, anyway? > > > > > > Nothing is allowed to happen at noon in either experiment. > > > > Nothing "happens" at noon? I take this to mean that there is no > > insertion or removal of balls at noon, yes? Well, I agree with that. > > Hmm. Yes, there is no ball whose insertion time or removal time is > noon. But it seems to me that this "happen" is underdefined in a way > that can cause confusion. Does something "happen" to either of these > functions at x=0: > > f(x) = 1 if x<0 ; 0 if x>=0 > > g(x) = 1 if x<=0 ; 0 if x>0 > > It seems to me that it is true (within the accuracy of normal > communication) to say that both f() and g() "drop from 1 to 0 at x=0" > even though the functions are different. > > Similarly, it seems to me that clearly something "happens" (in any > normal sense) at noon in the standard vase problem - what happens is > that the frenzy of unending sequences of insertion and removal come to > a halt. > And it follows by TO's unspoken assumptions that if something happens at noon, then there is some other thing that /caused/ it to happen at noon. But since nothing specified in the problem statement happens /at/ noon which causes the frenzy to stop (it simply mysteriously stops) we come to the conclusion: noon is a time when things happen without cause. Which is an absurd thing to say about a time; so either noon cannot properly be said to be an actual time at all ("noon doesn't exist/occur/happen"); or else something not specified in the problem actually does happen at noon (such as the removal/addition of an infinite number of infinitely labelled balls); or else the stopping of the frenzy and its cause both occur at a time which is strictly between all times before noon and noon itself (in which case, nothing happens at all /at/ noon; instead, something happens at a time which is indistinguishable from, but not the same as, noon). This is where/how Tony leaves the rails. The examples you give above of f(x) and g(x) are irrelevant; because there is no specified "physical action" (ball removal or insertion) in those examples; so the problem of "happenings" and "causes" is not an issue; f and g are simply distractions from the original problem. On the other hand, we can say that f(x) "correctly captures" the removal of a single ball /at/ time 0, whereas g(x) can't capture any such a thing; the ball would have to be removed /at/ some time strictly between all times after 0, and 0 itself (although on reflection, this may or may not be possible in Tony's worldview, which is hardly consistent). Cheers - Chas
From: Lester Zick on 1 Nov 2006 17:26 On 31 Oct 2006 10:00:15 -0800, "David R Tribble" <david(a)tribble.com> wrote: >[Apologies if this duplicates previous responses] > >Tony Orlow wrote: >> I am beginning to realize just how much trouble the axiom of >> extensionality is causing here. That is what you're using, here, no? The >> sets are "equal" because they contain the same elements. > >Yes, the basic definition of set equality, the '=' set operator. > >> That gives no >> measure of how the sets compare at any given point in their production. > >This makes no sense. Sets are not "produced" or "generated". >Sets simply exist. "Simply" being the operative word. ~v~~
From: Lester Zick on 1 Nov 2006 17:27
On 31 Oct 2006 15:08:45 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: > >> Whereas you just shoot off your small mouth, Moe, and whine when you >> get called on it. > >A vaccuous claim. Nature(x)abhors(x)vac(x)cuous(x)claims(x). ~v~~ |