An uncountable countable set
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From: Lester Zick on 1 Nov 2006 17:33 On 31 Oct 2006 15:29:31 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: >> >There's nothing I left out that justifies representing me as having >> >claimed that there is a proof that there is no consistent theory. >> >> Thanks. I guess we'll just have to take your word for it. > >The burden is not on me to show that I didn't claim that there's a >proof that there is no consistent theory. Yeah(x).Whatever(x).Then(x)I(x)guess(x)the(x)burden's(x)on(x)nobody(x). ~v~~
From: MoeBlee on 1 Nov 2006 17:59 Lester Zick wrote: > >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. True. But so what? I don't know of anyone who claims that the mere fact that there are different kinds of numbers is what enables set theory to be a foundation. MoeBlee
From: David Marcus on 1 Nov 2006 19:17 cbrown(a)cbrownsystems.com wrote: > imaginatorium(a)despammed.com wrote: > > 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). I've been trying to run the discussion in reverse (although with limited success). Suppose we start with this math: For j = 1,2,..., let a_j = -1/floor((j+9)/10), b_j = -1/j. For j = 1,2,..., define a function f_j: R -> R by f_j(x) = 1 if a_j <= x < b_j, 0 if x < a_j or x >= b_j. Let g(x) = sum_j f_j(x). What is g(0)? I would think that people would agree that g(0) = 0, even if they don't agree that this is the math that is equivalent to the English of the balls and vase problem. But, if they don't agree this is the equivalent math, my question to them is how would they translate this math into an English problem of a vase, balls, and time? I'd like to see how the result would differ from the standard balls and vase problem. On the other hand, Tony said that g(0) = oo. -- David Marcus
From: MoeBlee on 1 Nov 2006 19:18 Lester Zick wrote: > >> Yeah, yeah, I tell you what Moe: why don't you just stop talking about > >> it? I made reference to something you claimed which you can't justify > >> according to the posts you've mangled (intentionally it seems) and now > >> you're embarrassed about it. You're a big boy. Get over it already. > > > >I have not mangled any posts, intentionally or otherwise. > > Then(x)why(x)are(x)we(x)even(x)discussing(x)the(x)point(x)? Because(~v~~)you(~v~~)continue(~v~~)to(~v~~)make(~v~~)stupid(~v~~)comments(~v~~)related(~v~~)to(~v~~)it(~v~~). MoeBlee
From: David R Tribble on 1 Nov 2006 19:30
Tony Orlow wrote: > Find limits of formulas on numbers, not limits of sets. > > Here's what I said to Stephen: > > out(n) is the number of balls removed upon completion of iteration n, > and is equal to n. > > in(n) is the number of balls inserted upon completion of iteration n, > and is equal to 10n. > > contains(n) is the number of balls in the vase upon completion of > iteration n, and is equal to in(n)-out(n)=9n. > > n(t) is the number of iterations completed at time t, equal to floor(-1/t). > > contains(t) is the number of balls in the vase at time t, and is equal > to contains(n(t))=contains(floor(-1/t))=9*floor(-1/t). > > Lim(t->-0: 9*floor(-1/t)))=oo. The sum diverges in the limit. > > See how that all fits together? Its almost like physics, eh? Where is the part that mentions the time the balls are inserted and the time the balls are removed? Where is your 't' of physics? |