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1 2005-09-28.txt:21:57:24: <Wildhalcyon> Im working on the mechanics for the word "lots" right now. It roughly means "uncountable" - so if you say "There are lots of lights" there are more than enough for any task you could possibly use them for. Think of "lots" as aleph-null
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2 2005-11-03.txt:04:34:41: <GregorR> All the numbers between 0 and 3 is (uncountably) infinite.
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3 2006-06-04.txt:17:28:17: <jix> yeah you get uncountable inifinite many positions
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4 2006-08-06.txt:01:24:37: <Razor-X> You still have an uncountable number of elements, but if you have an infinity of infinities, it's intuitively easy to see that this set has more than an infinity of elements....
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5 2006-08-06.txt:19:22:20: <ihope> Apparently the number of quantum gates is uncountable, and QBF is countable in every way, I think...
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6 2006-09-06.txt:00:28:03: <ihope> If you need uncountably many, you're on your own.
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7 2007-05-04.txt:01:04:06: <lament> however, you do have uncountable free time :)
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8 2007-05-04.txt:01:43:45: <pikhq> As is distance. That doesn't mean that distance is uncountable.
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9 2007-07-07.txt:23:14:36: <ihope> What if the range is uncountable?
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10 2007-07-07.txt:23:14:44: <oklopol> oerjan: if it's a real -> real function, that's uncountable as ihope said
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11 2007-07-07.txt:23:14:50: <oerjan> computable things are not uncountable
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12 2007-08-01.txt:22:02:16: <ihope> Yes, but I can't turn on an uncountably infinite number of points.
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13 2007-08-11.txt:23:45:14: <oklokok> can an ISM solve the halting problem of a superturing machine in uncountable time? :P
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14 2007-12-02.txt:03:03:54: <oerjan> an uncountable number in fact
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15 2008-02-01.txt:17:31:19: <ais523> uncountably infinite, in fact
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16 2008-03-21.txt:23:26:14: <ais523> because it can perform uncountably many computations in parallel
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17 2008-05-10.txt:21:13:13: <SimonRC> an uncountable stack of rules might work too
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18 2008-06-08.txt:19:52:46: <Slereah7> Uncountable sets are for non-constructive math.
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19 2008-06-08.txt:20:26:34: <augur> are we sure that real numbers are uncountably infinite?
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20 2008-06-28.txt:00:47:30: <oerjan> aleph 1 is the cardinal of the first uncountable ordinal, which is again fairly concretely the _set_ of countable well-ordering classes
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21 2008-09-18.txt:22:33:01: <ais523> Proud starts by creating an uncountably infinite number of threads
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22 2008-11-19.txt:20:50:28: <Deewiant> I've never seen das Zeug in itself mean anything other than "stuff" as an uncountable
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23 2008-11-19.txt:20:52:10: <Deewiant> uncountable. :-P
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24 2008-11-19.txt:20:53:17: <Deewiant> "uncountable." » "like, singular? no, that's not right." » "uncountable". » "yeah"
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25 2008-11-19.txt:20:55:23: <oklopol> well anyway, i haven't seen it used as an uncountable
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26 2008-11-19.txt:21:01:02: <Deewiant> yep, and that's uncountable. Or a meaning I'm unaware of. :-P
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27 2008-12-01.txt:16:55:36: <ais523> Proud's like I suggested but with an uncountably infinite set of assumptions
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28 2008-12-23.txt:15:07:09: <oklopol> now, because these numbers are infinitesimally small, we will do an uncountable number of cycles
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29 2009-01-07.txt:20:21:34: <oerjan> SPAWNS UNCOUNTABLE OFFSPRING
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30 2009-01-25.txt:00:11:26: <oklopol> kerlo: so you need an uncountable amount of them to get anything done
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31 2009-03-24.txt:00:06:13: <ehird> Oh, and on the topic of pseudomath, I used to try and fit uncountable sets into countable ones.
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32 2009-03-27.txt:04:39:41: <oklowob> and then one of the comments said something about uncountable sets
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33 2009-04-17.txt:23:05:01: <oklopol> first of all O(n^e) does not have a lower bound, when e is a real number, so while there's a lower bound for it, O(n), there is an uncountable number of possible small upper bounds.
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34 2009-05-09.txt:03:25:07: <Gracenotes> easy peasy once you're comfortable. same with monads, and uncountable other language features
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35 2009-05-09.txt:03:25:31: <GregorR> Uncountably finite?
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36 2009-05-23.txt:21:33:08: <ehird> oerjan: if you devoted the whole universe - or most of it, anyway - to the calculation of an ShaFuck program, and let it run for uncountable eons, then you could generate a program
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37 2009-06-09.txt:10:26:53: <ais523> there's an uncountable number of real numbers
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38 2009-07-26.txt:21:08:24: <AnMaster> ehird, oh right. Did I treat "effects" as an uncountable?
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39 2009-07-26.txt:21:09:02: <AnMaster> ehird, indeed as an uncountable then
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40 2009-07-26.txt:21:09:20: <AnMaster> ehird, uncountable: like "water" or "milk" (you can't say, "a"/"an" about them)
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41 2009-08-06.txt:00:14:50: <ehird> and uncountably infinitely many unstupid ones, but I wouldn't expect you to hit one :P
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42 2009-08-13.txt:23:50:22: <oklofok> yes, every game lasts for an uncountable amount of turns
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43 2009-08-13.txt:23:58:10: <ehird> [23:50] oklofok: yes, every game lasts for an uncountable amount of turns
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44 2009-10-15.txt:13:44:21: * AnMaster suspects uncountably infinite at least.
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45 2009-12-05.txt:22:33:14: <uorygl> If a function were just an expression with a free variable, there wouldn't even be uncountably many functions.
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46 2009-12-12.txt:16:17:52: <AnMaster> oerjan, so example of uncountable but well ordered set
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47 2009-12-12.txt:16:19:02: <oerjan> aleph-1, being the first uncountable ordinal, is the smallest example
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48 2010-01-19.txt:20:34:26: <cpressey> Ah, well. Is your velocity *countably* infinite or *uncountably* infinite? Which aleph are we talking about, here?
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49 2010-02-03.txt:08:46:32: <oklopol> i mean you can't sum over all the paths, there's an uncountable number of them
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50 2010-02-03.txt:08:49:00: <oklopol> all the possible turns is still an uncountable amount; and is this in R^3?
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51 2010-02-05.txt:06:12:34: <oklopol> http://knol.google.com/k/are-real-numbers-uncountable#
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52 2010-02-05.txt:19:28:48: <cpressey> Well, can you have closures of uncountable sets?
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53 2010-02-05.txt:19:29:35: <oklopol> topology is all about uncountability
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54 2010-02-05.txt:19:31:12: <oklopol> "can you take the closure of an uncountably large set w.r.t. some operation"
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55 2010-02-05.txt:19:33:12: <cpressey> So you have a graph with n nodes, and for each node there's a (potentially) uncountable set of infinite paths that starts at it.
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56 2010-02-05.txt:20:11:03: <cpressey> Er, and I realize now I was possibly saying something much uglier. (Every node of the tree would have an uncountable number of branches. That's overkill.)
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57 2010-02-05.txt:20:16:28: <oklopol> yeah i know you did, but i didn't, i said there'd be an uncountable amount of paths, because for some reason i thought the infinite paths would be there too
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58 2010-02-13.txt:14:48:48: <alise> http://knol.google.com/k/john-gabriel/are-real-numbers-uncountable/nz742dpkhqbi/10#
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59 2010-02-18.txt:23:06:18: <AnMaster> <cpressey> "Execution of instructions in one program induces execution of instructions in another, nearby program." Yes. <-- I first thought "what are you messing around with by doing induction over an uncountable set"
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60 2010-02-19.txt:05:27:34: <oerjan> <AnMaster> <cpressey> "Execution of instructions in one program induces execution of instructions in another, nearby program." Yes. <-- I first thought "what are you messing around with by doing induction over an uncountable set"
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61 2010-02-19.txt:05:29:31: <oerjan> however, you need to well-order the set first, and for most frequently used uncountable sets (reals, complexes) that requires using the axiom of choice. so you don't get any concrete sense of what the order is.
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62 2010-02-19.txt:15:03:11: <oerjan> 21:27:34 <oerjan> <AnMaster> <cpressey> "Execution of instructions in one program induces execution of instructions in another, nearby program." Yes. <-- I first thought "what are you messing around with by doing induction over an uncountable set"
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63 2010-02-19.txt:15:03:18: <oerjan> 21:29:31 <oerjan> however, you need to well-order the set first, and for most frequently used uncountable sets (reals, complexes) that requires using the axiom of choice. so you don't get any concrete sense of what the order is.
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64 2010-02-20.txt:12:15:53: <alise> "The obvious answer is that you took a computational specification of a human brain, and used that to precompute the Giant Lookup Table. (Thereby creating uncounted googols of human beings, some of them in extreme pain, the supermajority gone quite mad in a universe of chaos where inputs bear no relation to outputs. But damn the ethics, this is for philosophy.)"
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65 2010-02-20.txt:16:22:15: <oerjan> MissPiggy: this leads easily to a contradiction if you have uncountably many alternatives
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66 2010-02-20.txt:16:22:53: <MissPiggy> uncountable sample space
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67 2010-02-20.txt:17:02:04: <oerjan> that's my intuition on that anyway - the distinction between probability 1 and surely is only needed because of uncountability stuff
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68 2010-02-20.txt:17:03:44: <MissPiggy> I don't think there's any evidence for that rather than uncountable
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69 2010-02-20.txt:17:05:09: <MissPiggy> how can you have it certinaly happening in a countable subset, but we're not sure if it will in an uncountable one..
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70 2010-02-20.txt:21:46:06: <AnMaster> (I suspect this is non-computable and/or uncountable)
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71 2010-02-20.txt:21:49:41: <AnMaster> anyway I maintain that the set of all possible pages including all possible linked pages as data urls is uncountable
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72 2010-02-20.txt:22:06:52: <oklopol> AnMaster: if you have infinite pages, then there can obviously be uncountably many
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73 2010-02-26.txt:22:23:00: <uorygl> You know, the union of all countable ordinal numbers is uncountable, but there's a countable set that has all the countable ordinal numbers as subsets.
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74 2010-02-27.txt:06:30:49: <uorygl> There are countable models of ZFC. Such models must contain uncountable sets. Contradiction?
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75 2010-02-27.txt:06:31:12: <uorygl> No; an "uncountable set" in the model is really just a set where the enumeration is not in the model.
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76 2010-03-01.txt:13:27:24: <alise> my favourite bit of the GAZP vs. GLUT article is "The obvious answer is that you took a computational specification of a human brain, and used that to precompute the Giant Lookup Table. (Thereby creating uncounted googols of human beings, some of them in extreme pain, the supermajority gone quite mad in a universe of chaos where inputs bear no relation to outputs. But damn the ethics, this is for philosophy.)"
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77 2010-03-01.txt:17:03:51: <alise> so we should represent the turkey bomb universe as an infinite (uncountably so?) data structure
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78 2010-03-01.txt:17:11:05: <alise> [17:03] alise: so we should represent the turkey bomb universe as an infinite (uncountably so?) data structure
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79 2010-03-12.txt:16:06:49: <AnMaster> fax, why is it called finite analysis if it works on R, (an uncountably infinite set)..
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80 2010-03-20.txt:13:58:43: <AnMaster> at least for uncountable sets
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81 2010-04-04.txt:18:00:04: <AnMaster> now I want an uncountably infinite bf tape :(
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82 2010-04-09.txt:16:33:06: <alise> *If you want the and uncountable billions of years of suffering, you can use D.
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83 2010-04-25.txt:01:04:52: <oerjan> and for an _uncountable_ set like the interval [0,1], it's just the usual "every number has probability 0" "paradox" (resolved by having only countable additivity of probabilities.)
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84 2010-05-16.txt:10:54:02: <AnMaster> oerjan, can't you get a bijection between uncountable of same cardinality?
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85 2010-05-19.txt:19:21:55: <oerjan> AnMaster: well a continuous circle is uncountable, so...
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86 2010-06-04.txt:23:51:16: <alise> uncountable aeons ago
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87 2010-06-21.txt:21:59:28: <Phantom_Hoover> Uncountability almost certainly factors into it.
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88 2010-06-21.txt:21:59:29: <AnMaster> cpressey, both are uncountably infinite, could be tricky to diagonalize?
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89 2010-06-21.txt:22:21:04: <AnMaster> oerjan, countable and uncountable?
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90 2010-06-21.txt:22:21:31: <AnMaster> if that is true countable == uncountable which is not true afaik?
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91 2010-06-21.txt:22:22:08: <oerjan> AnMaster: um no, there is an unending (in fact itself uncountable) collection. 2^M has larger size than M, always (Cantor diagonalization)
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92 2010-06-21.txt:22:24:25: <oerjan> s/infinitely/uncountable/, really
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93 2010-06-22.txt:16:11:12: <Phantom_Hoover> Hence implying that they are also uncountably infinite?
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94 2010-06-22.txt:18:47:50: <oklopol> but umm computable reals being uncountable
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95 2010-06-22.txt:18:53:06: <oklopol> the computable reals are computably uncountable
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96 2010-06-22.txt:19:50:35: <oklopol> oerjan and i have to talk about computable uncountability now
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97 2010-06-22.txt:19:51:02: <oklopol> yes, the computable reals are computably uncountable
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98 2010-06-22.txt:20:14:30: <oklopol> if the sets can be uncountable then...
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99 2010-06-23.txt:19:52:42: <AnMaster> oklopol, if there is no holes in space it basically mean you will have an uncountable set?
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100 2010-06-23.txt:20:08:45: <oklopol> (i'm joking, there are uncountably many)
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101 2010-06-23.txt:20:15:06: <oklopol> for uncountability (in the real case), notice you can add small enough fluctuations to each element of the sequence
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102 2010-06-25.txt:23:11:12: <AnMaster> pikhq, well it could be going to uncountable infinite then </technobable>
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103 2010-06-25.txt:23:11:43: <AnMaster> oerjan, also do you highlight on uncountable or something?
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104 2010-07-24.txt:22:55:40: <Phantom_Hoover> But surely that makes them uncountable?
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105 2010-07-29.txt:23:10:54: <Phantom_Hoover> I like using "error" as an uncountable noun.
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106 2010-09-04.txt:01:49:02: <oerjan> Sgeo: is it countable or uncountable?
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107 2010-09-04.txt:01:49:27: * Sgeo wonders if "uncountably finite" makes sense
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108 2010-09-04.txt:01:50:09: <zzo38> Sgeo: It only make sense if what you mean by "uncountably" is that it is too long to count and you don't have time or words for them
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109 2010-09-04.txt:01:50:30: <zzo38> But that is probably not what is meant, because it isn't what it meant in "uncountably infinite"
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110 2010-09-04.txt:01:54:44: <cpressey> * Sgeo wonders if "uncountably finite" makes sense <-- Thank you; you are justifying "very strange"
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111 2010-09-04.txt:01:55:15: <cpressey> 1, 2, 3... ah, shit, I'm bored. Well, I guess that the numbers on the clock are uncountably finite.
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112 2010-09-04.txt:01:56:34: <oerjan> in a sense such a set is uncountable (not equivalent to a subset of naturals) but still finite in the other sense
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113 2010-09-04.txt:02:02:54: * Sgeo happies oerjan for allowing "uncountably finite" to exist
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114 2010-09-05.txt:04:05:47: <Sgeo> Is there an uncountable infinite discreet space? A countably infinite continuous space? Or are these axiomatically tied in, or is there a theorem?
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115 2010-09-05.txt:04:09:27: <oklofok> "Is there an uncountable infinite discreet space?"
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116 2010-09-05.txt:04:09:41: <oklofok> take an uncountably infinite set X
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117 2010-09-05.txt:04:10:52: <oklofok> and it's uncountable because X is
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118 2010-09-08.txt:17:20:17: <fizzie> It wouldn't even necessarily need a symlink in ~, just something to generate /tmp/foo for each user, and set TMPDIR to that. Though I'm sure there's an uncountable number of apps that have "/tmp" hardcoded.
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119 2010-09-14.txt:22:33:57: <Vorpal> uncountable keyboard?
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120 2010-09-18.txt:23:52:13: <Vorpal> to me code in the sense of "source code" is uncountable
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121 2010-11-04.txt:14:12:22: <Vorpal> the states for the bignum case would be uncountable, while for the bit case they would be countable, no?
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122 2010-11-10.txt:17:00:54: -!- Sgeo changed the topic of #esoteric to: ASIEKIERKA FOREVER | http://tunes.org/~nef/logs/esoteric/?C=M;O=D | amount of topic spam: uncountably infinite
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123 2010-11-12.txt:15:37:18: <Sgeo> I was about to confusedly ask something along the lines of "Is the amount of infinite sets of rationals uncountably infinite somehow? Because if not, I don't see how reals defined in terms of Dedekind cuts are uncountably infinite"
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124 2010-11-12.txt:15:37:46: <Sgeo> But then, I _think_ the diagonalization thingy says that there is an uncountably infinite amount of those sets
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125 2010-11-12.txt:15:39:30: <oklopol> Sgeo: the amount of infinite subsets of rational numbers is uncountable
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126 2010-11-12.txt:15:40:19: <oklopol> well there's an uncountable number of subsets of integers
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127 2010-11-12.txt:20:38:59: <elliott> angst (uncountable)
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128 2010-11-12.txt:20:39:29: <oklopol> haha elliott has an uncountable amount of angst
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129 2010-11-12.txt:20:39:52: <elliott> cheater99: "homophobia (uncountable)
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130 2010-11-16.txt:01:53:23: <Sgeo> On http://en.wikipedia.org/wiki/Uncountably_infinite
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131 2010-11-30.txt:12:45:43: <Phantom_Hoover> 22:15:14 <oerjan> interestingly, if you had a library of all possible text files arranged alphabetically, _finding_ anything interesting in it would be as hard as inventing it yourself ← surely the set of all possible text files is uncountably infinite?
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132 2010-11-30.txt:12:49:24: <oerjan> <Phantom_Hoover> 22:15:14 <oerjan> interestingly, if you had a library of all possible text files arranged alphabetically, _finding_ anything interesting in it would be as hard as inventing it yourself ← surely the set of all possible text files is uncountably infinite?
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133 2011-01-13.txt:19:06:49: <Vorpal> in my country you can drive an uncountable infinity distance
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134 2011-01-13.txt:23:02:16: <pikhq> The issue with "VIRII" as a plural for "VIRUS" is that in Latin, "VIRUS" is an uncountable noun.
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135 2011-01-13.txt:23:03:11: <Phantom_Hoover> At least with comparison to their entry for arma, which I *know* is an uncountable noun.
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136 2011-01-23.txt:00:21:44: <oklofok> then don't we just get the usual kinds of configurations over Z^2, but just an uncountable number of disjoint orbits
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137 2011-02-26.txt:23:19:57: <oklopol> (we'll take it as a given that any natural way to make a for-loop over the uncountable set of points gives us the right answer)
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138 2011-03-09.txt:01:31:06: <quintopia> up to the point of showing 2^N is uncountable
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139 2011-03-12.txt:22:32:12: <Phantom_Hoover> How do you have an uncountably infinite tree?
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140 2011-03-12.txt:22:32:57: <Zwaarddijk> what would be interesting would be if someone managed to abuse terminology cleverly enough to get an uncountably finite something
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141 2011-03-12.txt:22:39:04: <ais523> I don't see why that would make it uncountable
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142 2011-03-12.txt:22:47:47: <Phantom_Hoover> Zwaarddijk, conclusion: *all* finite sets are uncountable.
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143 2011-03-12.txt:22:58:36: <Phantom_Hoover> To allow uncountable finite sense.
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144 2011-03-12.txt:22:59:12: <oerjan> Phantom_Hoover: well without the axiom of choice you can have uncountably finite sets, as said
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145 2011-03-13.txt:12:16:30: <elliott> 23:15:28 <Phantom_Hoover> How do you have an uncountably infinite tree?
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146 2011-03-13.txt:12:19:44: <oklopol> "[14:00:45] <elliott> 23:15:28 <Phantom_Hoover> How do you have an uncountably infinite tree?" by having one?
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147 2011-03-13.txt:12:23:37: <oklopol> if a tree is uncountable, then of course there even has to be a vertex of uncountable degree, because a countable union of countable sets is countable
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148 2011-03-13.txt:12:42:20: <cpressey> '<oklopol> "[14:00:45] <elliott> 23:15:28 <Phantom_Hoover> How do you have an uncountably infinite tree?"' <- have a countably infinite number of branches at each node? at a guess.
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149 2011-03-13.txt:12:44:45: <oklopol> but the point is connectivity is defined by finite paths, so connected components will be countable unless you have uncountable degrees locally, somewhere
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150 2011-03-13.txt:12:47:20: <cpressey> oklopol: er - what if you have a root node, with a countably infinite number of children, but they're all leafs? that's not uncountable
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151 2011-03-13.txt:12:48:00: <cpressey> oh, if you have UNcountably infinite branches at one node, then yes the tree is uncountable :)
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152 2011-03-13.txt:12:48:04: <oklopol> you will have to have at least one node with uncountable degree
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153 2011-03-13.txt:12:52:33: <Phantom_Hoover> cpressey, are you confused as to countable vs. uncountable infinity?
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154 2011-03-13.txt:12:56:06: <Phantom_Hoover> cpressey, FWIW, the *set* of all infinite graphs is uncountable.
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155 2011-03-13.txt:13:38:47: <cpressey> oklopol: oh, i just saw why that tree thing isn't uncountable :)
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156 2011-03-20.txt:14:56:00: <oklopol> you can apply that... what's 4 times uncountable?
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157 2011-03-20.txt:14:56:40: <oklopol> but it's divisible by two, so maybe you could prove the claim for p*uncountable where p is a prime first, and then show the the numbers that satisfy it are closed under multiplication
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158 2011-03-21.txt:21:38:09: <oklopol> pikhq_: yeah right, next u gonna say the reals are uncountable lol
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159 2011-03-21.txt:22:10:27: <cheater-> uncountably many.
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160 2011-03-21.txt:22:10:49: <Phantom_Hoover> It's uncountable, actually.
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161 2011-03-21.txt:22:11:15: <rapido> i don't like infinite/uncountable stuff - but hey - i'' make an exception
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162 2011-03-21.txt:23:22:07: <oklopol> iterations implies countable, and cantor set implies uncountable space
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163 2011-03-21.txt:23:23:05: <oklopol> and ultrafilters are rather fucking big in uncountable spaces so that obviously cannot happen
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164 2011-03-29.txt:17:52:59: <Phantom_Hoover> Hmm, the Cantor set is uncountable?
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165 2011-03-29.txt:17:57:28: <oerjan> also, yes the cantor set is uncountable, same cardinality as the real numbers or the interval [0,1].
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166 2011-04-21.txt:04:43:42: <oklopol> elliott: i meant more like, for each ordinal, you define a partially filled board by taking the union of all the last ones and then applying the player functions in succession, then play until the first uncountable ordinal
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167 2011-04-21.txt:19:23:16: <crystal-cola> http://qchu.wordpress.com/2009/11/05/i-dont-trust-uncountable-sets/
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168 2011-04-21.txt:20:17:08: <oklopol> elliott: every time a black hole and a white hole are joined in holy matrimony, an uncountable set is born
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169 2011-04-22.txt:16:28:22: <Gregor> Y'know, even though I've typed "unsigned char" uncountably many times, it makes more sense for it to be signed by default, since that's consistent with all the other types.
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170 2011-06-01.txt:02:11:07: <CakeProphet> ptr+1 points to the next char in the string, and all of the bytes of the infinite width char are represented as decimal points (but then they become uncountable, which is another problem I think)
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171 2011-06-10.txt:23:18:15: <oklofok> If a space is metrizable, then it is sequentially compact if and only if it is compact. However in general there exist sequentially compact spaces which are not compact (such as the first uncountable ordinal with the order topology), and compact spaces which are not sequentially compact (such as the product of uncountably many copies of the closed unit interval).
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172 2011-06-13.txt:00:02:03: <elliott> but the reals are uncountable
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173 2011-06-13.txt:00:02:10: <elliott> uncountable > countable
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174 2011-06-13.txt:00:05:28: <CakeProphet> I wonder what would be required of strings to produce an uncountable number of them.
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175 2011-06-13.txt:00:07:28: <oerjan> CakeProphet: infinite (but still countable) length noncomputable strings are uncountable
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176 2011-06-21.txt:02:48:39: <zzo38> MWI is not really multiple worlds. It is like all uncountable possibilities.
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177 2011-06-23.txt:06:08:44: <elliott_> then there are uncountable theorems
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178 2011-06-23.txt:06:14:52: <coppro> if the model has an uncountable member, the set of truths be uncountable
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179 2011-06-23.txt:06:32:35: <CakeProphet> well, if we could prove that uncountable sets are also interesting, and that cardinality of a set corresponds to more interesting sets
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180 2011-06-23.txt:06:42:24: <Sgeo_> Involve an infinite number of natural numbers, _then_ it's uncountable
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181 2011-06-23.txt:06:43:51: <CakeProphet> ....? but aren't rational numbers a quotient of /any/ (read: from an infinite set of natural numbers) integers? According to what Sgeo_ says that would make rational numbers uncountable?
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182 2011-06-23.txt:06:45:15: <elliott_> CakeProphet: the set of infinite lists of naturals is uncountable.
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183 2011-06-23.txt:06:45:47: <Sgeo_> Now, if you had infinite number of dimensions, even though each dimension can only take integer values, the number of points is uncountably infinite
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184 2011-06-23.txt:06:47:29: <Sgeo_> The reals are uncountably infinite, even though each digit can only have 1 of 10 values.
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185 2011-06-27.txt:13:08:16: <elliott> uncountably infinite spheres
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186 2011-06-27.txt:14:38:20: <elliott> Gregor: It would be kind of impossible what with the uncountably infinite thing :P
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187 2011-07-17.txt:05:35:47: <oklofok> note that unions can be arbitrary, you could even have an uncountable number of open sets that you're taking the union of
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188 2011-07-19.txt:20:37:42: <oklopol> "<Taneb> But theoretically, there are only a finite number of possible games of Go" <<< depends on endgame rules, i think some of them might let you have an uncountable number of games?
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189 2011-07-19.txt:20:51:51: <oklopol> ais523: alright. then just add some possible move in the middle and you'll have uncountably many games.
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190 2011-07-19.txt:21:12:53: <coppro> oklopol: I've never heard of any rules of Go which would lead to an uncountable number of games
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191 2011-07-19.txt:21:15:22: <ais523> because you can interleave them uncountably many ways
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192 2011-07-19.txt:21:16:15: <ais523> thus, uncountably many games are possible
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193 2011-07-22.txt:20:59:50: <Sgeo> (I thought maybe you could enumerate through all uncountably infinite states of an infinite 2d binary grid by starting at one point, on and off, then expanding it, etc. I finally realized that those are counting through finite pieces of the grid, not the actual infinite grid
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194 2011-08-09.txt:20:52:58: <NihilistDandy> "I proved that the reals are uncountably infinite. Where? There, diagonally. Pretty sneaky, sis."
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195 2011-08-19.txt:23:49:18: <CakeProphet> okay so, I'm pretty sure the number of Haskell linked lists in uncountable, but how would you prove this?
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196 2011-09-06.txt:07:25:41: <zzo38> On the wall, I have the picture of creature with one eye and uncountable tentacles. Not because there is too many to count; it is because the artist draw the picture to make it difficult.
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197 2011-09-14.txt:04:27:25: <oklopol> if a tiling never repeats itself, you have uncountably many ways to tile the plane
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198 2011-09-14.txt:04:27:47: <oklopol> i mean if there is no periodic tiling, then you have uncountably many tilings
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199 2011-09-14.txt:04:29:20: <oklopol> Therefore, a finite patch cannot differentiate between the uncountably many Penrose tilings, nor even determine which position within the tiling is being shown.[43]
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200 2011-09-14.txt:04:37:12: <oklopol> Patashu: i can easily prove the uncountability thing to you if you know what compactness is, otherwise i'll go to work
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201 2011-10-12.txt:10:36:29: <CakeProphet> how does that lead to uncountability?
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202 2011-10-12.txt:10:37:22: <oerjan> CakeProphet: the number of sets of rationals is uncountable, for a start.
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203 2011-10-12.txt:10:39:30: <oerjan> for the rest, see an actual uncountability proof.
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204 2011-10-24.txt:07:46:56: <elliott> `addquote <coppro> clearly darth needs something gray and big and proving the uncountability of the reals
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205 2011-10-24.txt:07:47:03: <HackEgo> 691) <coppro> clearly darth needs something gray and big and proving the uncountability of the reals
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206 2011-10-25.txt:23:18:50: <oklopol> i'm actually playing continuous path on it all day long, which is uncountably infinite times cooler.
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207 2011-11-12.txt:22:00:22: <oerjan> the latin virus is an uncountable noun, so any weird plural is suspect.
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208 2011-12-02.txt:10:05:20: <kallisti> "So there are as many points in the Cantor set as there are in [0, 1], and the Cantor set is uncountable "
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209 2011-12-11.txt:00:57:52: <oerjan> of which there are uncountably many, in fact to-big-to-be-a-set many.
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210 2011-12-15.txt:16:22:08: <elliott> Someone should figure out exactly how much you can solve with a halting oracle; I'm pretty sure you can nest it to solve some statements about uncountable sets, but I don't think it can do everything.
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211 2012-01-07.txt:13:51:16: <Phantom_Hoover> oklopol, well, um, at the start of the game you have squares of piece (that's like piece but an uncountable noun) occupying the subset of [0,8]^2 corresponding to their initial positions in normal chess.
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212 2012-01-07.txt:20:08:24: <Vorpal> so anything else doesn't matter unless it is uncountable
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213 2012-01-11.txt:20:12:47: <kallisti> where I get learn about COUNTABLE AND UNCOUNTABLE SETS.
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214 2012-01-12.txt:19:01:34: <Ngevd> I'm pretty sure infinite-length strings are uncountable
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215 2012-01-12.txt:21:29:24: <Phantom_Hoover> 19:01:34: <Ngevd> I'm pretty sure infinite-length strings are uncountable
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216 2012-01-12.txt:21:33:07: <Phantom_Hoover> 19:01:34: <Ngevd> I'm pretty sure infinite-length strings are uncountable
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217 2012-02-05.txt:18:41:57: <fizzie> And apparently also the only possible winner, too. (530k uncounted votes, 660k lead.)
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218 2012-02-13.txt:00:06:23: <oklopol> or at the first uncountable ordinal
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219 2012-02-16.txt:23:51:53: <kallisti> fizzie: well you could make those parameters of a function and then see if the domain is uncountable.
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220 2012-03-09.txt:20:24:19: <elliott> augur: Why are you claiming that you have a bijection between a countable set and an uncountable set?
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221 2012-03-10.txt:03:10:34: <elliott> augur: i did; you clarified that it was actually a bijection between two countable sets, except the topic was whether you could use a method that requires an isomorphism to a specific _uncountable_ set
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222 2012-03-17.txt:11:13:29: <elliott> Phantom_Hoover: headache am uncountable noun
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223 2012-03-30.txt:19:04:16: <oklopol> alvur: do you believe in uncountable sets?
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224 2012-03-30.txt:19:06:52: <alvur> oklopol, there's nothing uncountable but God!
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225 2012-03-30.txt:19:09:55: <oklopol> i'm a uncountable set fundamentalist
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226 2012-03-30.txt:19:34:20: <Phantom_Hoover> <alvur> oklopol, there's nothing uncountable but God!
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227 2012-03-30.txt:19:47:13: <oklopol> oerjan: my ban finger started itching when he told me he doesn't believe in uncountable sets.
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228 2012-03-31.txt:22:36:12: <elliott> wait did Sgeo not know the reals were uncountable before today
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229 2012-03-31.txt:22:37:08: <ais523> elliott: they're exactly uncountable, they're no more than uncountable
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230 2012-04-16.txt:16:09:06: <Phantom_Hoover> Huh, the Chinese for 'card game' is uncountable.
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231 2012-04-28.txt:10:31:12: <oklopol> because euclidean space, that is, R^n for R the reals and n a natural number is uncountable, so you need to have at least the cardinality of reals
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232 2012-05-18.txt:03:00:52: <HackEgo> 646) <coppro> clearly darth needs something gray and big and proving the uncountability of the reals
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233 2012-05-19.txt:21:29:57: <Taneb> I'm going for uncountable
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234 2012-05-19.txt:21:33:11: <Taneb> If it's uncountable without putting 8s in other 8s, it will be uncountable with that ability
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235 2012-05-19.txt:21:33:28: <elliott> It's uncountable because you can imagine packing the reals the same way, Q.E.D..
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236 2012-05-19.txt:21:33:56: <shachaf> OK, so how is it uncountable without putting 8s in other 8s?
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237 2012-05-19.txt:21:53:34: <shachaf> OK, but how do you get uncountably many that way?
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238 2012-05-19.txt:22:05:36: <Sgeo> How would a packing problem have uncountably infinite pieces in a space?
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239 2012-05-19.txt:23:07:29: <oklofok> the idea is similar to the one for "uncountable sum of positive reals is infinite"
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240 2012-05-19.txt:23:10:14: <oklofok> similarly, for the eights, we note that if you take any "rational interval of 8 approximations", then some approximation interval is uncountable, which will be a contradiction. by an approximation interval i mean something like "height of the 8 is between x and y, and the angles in the middle are between z and w" or something.
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241 2012-05-19.txt:23:25:49: <oklofok> can no space with a nontrivial fundamental group have uncountably many nonoverlapping embeddings?
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242 2012-05-20.txt:00:24:11: <oklofok> "oklofok can no space with a nontrivial fundamental group have uncountably many nonoverlapping embeddings?" oookay wtf was i thinking :D
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