IRC/Quotes/Infinity
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A long discussion had in the #falasan channel on IRC on the nature of infinity between a few BM players. Too good not to record, too big to flood the main page with. It may contian rambling, nonsense, and dangerously to universe shattering amounts of philosophy and/or logic. Enjoy :-)
[23:15:14] <Reilwin> Nooo! I shall forever remain in this state of confusion and damnation, for eternity and infinity!!! [23:15:18] <Reilwin> :~( [23:15:37] <Reilwin> Cursed to remain in an unstable quantum state [23:15:53] <Reilwin> balanced between "yes" and "no" [23:15:58] <Reilwin> "1" and "0" [23:16:04] <Reilwin> "true" and "false" [23:16:10] <Reilwin> "good" and "bad" [23:16:16] <Reilwin> "a" and "z" [23:16:31] <Reilwin> "negative infinity" and "positive infinity" [23:16:35] <Reilwin> apples and oranges [23:16:49] <Reilwin> birds and fish [23:16:57] <Reilwin> pigs and crabapples [23:17:06] <Reilwin> flint and steel [23:17:12] <Reilwin> blue and red [23:17:16] <Reilwin> purple and green [23:17:21] <Reilwin> black and white [23:17:27] <Reilwin> sticks and stones [23:17:32] <Reilwin> breaks and bones [23:17:43] <Reilwin> ricks and phones [23:20:22] <Kel> hehe [23:20:53] <Reilwin> Will somebody provide an observation to collapse my quantum state? [23:21:11] <Reilwin> To bring my knowledge into being? [23:21:34] <Reilwin> to bring me back from the madness and insanity that is quantum physics? [23:21:52] <Reilwin> Or will I be left to rot and linger within the depths of quantum hell? [23:29:42] <SniperChief> there's negative infinity and positive infinity? [23:30:02] * SniperChief was under the impression that infinity, like 0, couldn't be positive or negative [23:31:45] <Reilwin> mathematically speaking [23:31:53] <Reilwin> and within the limits of certain fields [23:31:58] <Reilwin> such as the Real Numbers [23:32:08] <Reilwin> yes, there is a negative and positive infinity [23:32:25] <Reilwin> the positive infinity which is the set of all positive real numbers [23:32:37] <Reilwin> and the negative infinity which is the set of all negative real numbers [23:32:48] <Reilwin> replace "real" by the applicable field of your choice [23:33:23] -->| LoronzoGrey (~JoshHouck@c-71-224-172-175.hsd1.pa.comcast.net) has joined #falasan [23:33:46] <SniperChief> hmm [23:33:55] <LoronzoGrey> hi [23:34:27] <Reilwin> hmm [23:34:29] <Reilwin> hi [23:34:38] * Reilwin sniffs LoronzoGrey suspiciously [23:34:42] * SniperChief isnae convinced [23:34:49] <LoronzoGrey> sniffs? [23:35:05] <Reilwin> you aren't convinced? [23:35:13] <LoronzoGrey> why am i sniffed? [23:35:26] <Reilwin> Is your bio-AL-unit functioning correctly? [23:36:07] <Reilwin> you smell suspicious [23:36:14] <Reilwin> that's why you're sniffed :P [23:36:30] =-= Mode #falasan +v LoronzoGrey by Reilwin [23:36:40] * Reilwin pokes SniperChief [23:36:43] <LoronzoGrey> bio-AL-unit? [23:36:44] <Reilwin> Is your bio-AL-unit functioning correctly? [23:36:51] <SniperChief> I have no idea. [23:36:59] <SniperChief> least of my worries [23:37:48] <LoronzoGrey> ... [23:38:06] <Reilwin> Arithmetic/Logic unit [23:38:13] <Reilwin> <SniperChief> there's negative infinity and positive infinity? [23:38:23] <Reilwin> * SniperChief was under the impression that infinity, like 0, couldn't be positive or negative [23:38:27] <Reilwin> <Reilwin> mathematically speaking [23:38:27] <Reilwin> <Reilwin> and within the limits of certain fields [23:38:27] <Reilwin> <Reilwin> such as the Real Numbers [23:38:28] <Reilwin> <Reilwin> yes, there is a negative and positive infinity [23:38:28] <Reilwin> <Reilwin> the positive infinity which is the set of all positive real numbers [23:38:30] <Reilwin> <Reilwin> and the negative infinity which is the set of all negative real numbers [23:38:32] <Reilwin> <Reilwin> replace "real" by the applicable field of your choice [23:38:53] <Reilwin> when you say simply 'infinity' [23:39:09] <Reilwin> then it would be like saying 'the set of all real numbers' [23:39:16] <Reilwin> which includes both positive and negative [23:39:20] * SniperChief can see the logic, but given that he's used to quantifying infinity as 0 (on account of that being the average of infinity) isn't used to it [23:40:01] <Reilwin> How did you calculate the average of infinity? [23:40:06] <SniperChief> easy [23:40:11] <SniperChief> you start at 0 [23:40:29] <SniperChief> to put this in metaphor terms [23:40:32] <SniperChief> for every step you take forward [23:40:36] <SniperChief> you also take one back [23:40:50] <SniperChief> repeat, quite literally, ad infinitum [23:40:52] <Reilwin> but that's assuming that every step you take back [23:40:57] <SniperChief> is the same length? [23:40:58] <SniperChief> yes [23:41:00] <Reilwin> is equal to the number of steps you take forward [23:41:09] <SniperChief> it is. [23:41:18] <Reilwin> Which is a simplistic notion when you consider infinity, don't you think? [23:41:22] <SniperChief> nope. [23:41:29] <Reilwin> The formula for average is: (x+y)/2 [23:41:39] <Reilwin> however, infinity + infinity = infinity [23:41:44] <Reilwin> and infinity halved = infinity [23:41:47] <SniperChief> but it's infinity - infinity [23:41:53] <Reilwin> therefore the average of infinity is infinity [23:42:00] <Reilwin> my bad, it's subtracted [23:42:02] <SniperChief> your positive values versus negative values [23:42:09] <Reilwin> but subtraction of infinity is still infinity [23:42:23] <SniperChief> one infinity cannot be smaller than the other [23:42:26] <Reilwin> hum [23:42:29] <SniperChief> or it's just not infinity [23:42:34] <Reilwin> actually...it can [23:42:39] <SniperChief> as size relies on finity [23:42:47] <Reilwin> the infinity of all natural numbers, for example [23:42:51] <SniperChief> (bullsh*t neologism alert) [23:42:56] <Reilwin> is greater than the infinity of all real numbers [23:43:08] <Reilwin> the infinity of all even natural numbers [23:43:17] <Reilwin> is equal to the infinity of all natural numbers [23:43:29] <Reilwin> Heh, it's a proof in mathematics :P [23:43:33] <Reilwin> part of set theory [23:43:42] <Reilwin> consider this: [23:44:31] <Reilwin> The set of all natural numbers, N, is equal to the set of all odd numbers within N, which is also equal to the set of all even numbers within N [23:44:46] <Reilwin> the proof for it goes as follows: [23:45:10] * SniperChief is instantly thinking "it's 0" [23:45:17] <Reilwin> for every cardinal natural within N, the odd numbers within N, and the even numbers within N [23:45:23] <Reilwin> ... [23:45:25] <Reilwin> um [23:45:33] <Reilwin> the set of all Natural Numbers = infinity [23:45:36] <SniperChief> no, I know [23:45:42] <Reilwin> ok [23:45:56] <SniperChief> but if I claim that infinity,when taken as a number, is 0 (N here) the statement still works, right? [23:46:04] <SniperChief> there's no point arguing advanced mathematics with me [23:46:10] <SniperChief> I'm 16 and doing the AS maths course :P [23:46:30] <SniperChief> any understanding of infinity I have is what I've reasoned in my free time [23:46:31] <Reilwin> AS = ? [23:46:37] <SniperChief> advanced subsidiary [23:47:02] * Reilwin wonders if SniperChief is interested in Reilwin's proof or not [23:47:08] <SniperChief> oh, go for it [23:47:20] * SniperChief wikis cardinal number [23:48:56] <Reilwin> for every cardinal number within N, odd or even [23:49:02] <Reilwin> there is a matching ordinal number [23:49:28] <Reilwin> So: 1(1st), 2(2nd), 3(3rd)...within N [23:49:31] <SniperChief> ok [23:49:46] <Reilwin> 2(1st), 4(2nd), 6(3rd)...within E [23:50:00] <Reilwin> 1(1st), 3(2nd), 5(3rd)...within O [23:50:24] <Reilwin> hence, all the natural numbers are used up counting the even or odd numbers within N [23:50:34] <Reilwin> and although the even/odd numbers are part of N [23:50:39] <Reilwin> they're equal to N [23:50:53] <SniperChief> yeah [23:50:59] <Reilwin> although actually [23:51:02] <SniperChief> am I not accounting for that? [23:51:21] <SniperChief> because if you're saying N = E + O when N = E = O [23:51:29] <SniperChief> that works when N, E and O are all 0 [23:52:08] <SniperChief> ...I am so bugging my physics teachers about this next week. :P [23:52:17] <Reilwin> But then your average doesn't work either [23:52:27] <SniperChief> ? [23:52:28] <Reilwin> (0-0)/2 = 0 [23:52:32] <Reilwin> 0 = 0 = 0 [23:52:46] <SniperChief> what's not working? [23:53:14] <Reilwin> 0 != infinity, but if you use it in that arithmetic to symbolize infinity [23:53:26] <Reilwin> then you're saying that the average is equal to infinity [23:53:35] <SniperChief> oh, zero isn;t infinity at any finite point *on* infinity [23:53:52] <Reilwin> I'm not saying that zero is infinity [23:53:52] <SniperChief> or rather, any finite point on infinity is not neccesarily zero [23:54:02] <Reilwin> but you use it to symbolize infinity within your arithmetic [23:54:24] <SniperChief> nothing is everything and everything is nothing - it's some kind of zen :-) [23:54:39] <Reilwin> by arithmetic, I mean number operations [23:54:43] <Reilwin> +, -, *, / [23:54:45] <LoronzoGrey> okay [23:54:47] <SniperChief> I don't use infinity in mathematics [23:54:50] <LoronzoGrey> i walked in on a math discussion [23:54:52] <LoronzoGrey> yay [23:54:56] <LoronzoGrey> cliff notes please? [23:55:11] <Reilwin> You said you can use zero to manipulate infinity arithmetically [23:55:12] <SniperChief> LoronzoGrey: try http://simple.wikipedia.org/wiki/Infinity [23:55:15] <SniperChief> did I? [23:55:27] <LoronzoGrey> wait wait [23:55:29] <LoronzoGrey> i understand math [23:55:31] <LoronzoGrey> i mean [23:55:36] <LoronzoGrey> cliffnotes of the discussion [23:55:38] <LoronzoGrey> what is the question [23:56:00] <SniperChief> I'm basically comparing infinity and 0 [23:56:07] <Reilwin> hum [23:56:07] <LoronzoGrey> use limits [23:56:12] <Reilwin> nevermind, I see you didn't [23:56:25] <SniperChief> this is mostly a philoso [phical question for me [23:56:26] <Reilwin> but lemme pose you a question on your method for finding the average of infinity [23:56:39] <Reilwin> What tells you that you have to start your 'stepping' at 0? [23:56:40] <SniperChief> go for it [23:56:44] <Reilwin> Why not start at 100? [23:56:46] <Reilwin> Or -1? [23:56:50] <Reilwin> Or 17? [23:56:55] <SniperChief> because 0 is, by definition, the beginning [23:56:56] <Reilwin> Will the average remain the same, then? [23:57:05] <Reilwin> By definition? [23:57:11] <LoronzoGrey> Infinity has no start nor end [23:57:15] <Reilwin> . /your/ definition? [23:57:16] <LoronzoGrey> by its definition [23:57:19] <LoronzoGrey> it's undefinable [23:57:20] <SniperChief> no, but the number line does [23:57:26] <SniperChief> all numbers are relative to a point [23:57:27] <SniperChief> which is 0 [23:57:36] <LoronzoGrey> all numbers are relative to zero [23:57:39] <LoronzoGrey> infinity is not a number [23:57:41] <Reilwin> but that's just by convention [23:57:44] <SniperChief> which is why we had so much rouble in the history of maths coming up with the very conbcept of zero [23:57:44] <LoronzoGrey> its an abstract mathematical concept [23:57:50] <SniperChief> right [23:57:56] <SniperChief> Reilwin: you can start at 100 [23:58:04] <LoronzoGrey> then the average is 100 [23:58:05] <LoronzoGrey> so [23:58:06] <SniperChief> I should say rather that the distance you travl in hte infinite series is 0 [23:58:13] <Reilwin> SniperChief, the main problem in coming up with zero [23:58:19] <SniperChief> the average displacement is 0 [23:58:23] <SniperChief> not neccesarily where you are [23:58:26] <LoronzoGrey> because the average is where you begin to take your steps [23:58:29] <LoronzoGrey> which is subjective [23:58:32] <LoronzoGrey> so it's undefinable [23:58:32] <SniperChief> no it's not LoronzoGrey [23:58:36] <LoronzoGrey> so the average is infinity [23:58:37] <Reilwin> wasn't because people couldn't conceive of 'nothingness' [23:58:46] <LoronzoGrey> displacement is not average [23:58:46] <Reilwin> but rather because people thought of numbers as 'things' [23:58:50] <Reilwin> '3 lambs' [23:58:52] <Reilwin> '3 cows' [23:58:53] <SniperChief> I know [23:58:56] <Reilwin> '2 gold coins' [23:59:28] <Reilwin> '3 "things" ' didn't make sense, so there was no need for a number to represent 'no "things" ' [23:59:28] <LoronzoGrey> zero and infinity are inverse concepts [23:59:30] <SniperChief> LoronzoGrey: you;re making nosense mathmatically [23:59:38] <LoronzoGrey> how do you figure? [23:59:43] <LoronzoGrey> what did i say that made no sense? [23:59:50] <SniperChief> [23:58] <LoronzoGrey> because the average is where you begin to take your steps [23:59:52] <SniperChief> why? [23:59:58] <SniperChief> no it's not [00:00:00] <LoronzoGrey> take a seq [00:00:06] <SniperChief> if I start from zero, take 2 steps forward and one step back [00:00:06] <LoronzoGrey> with the center [00:00:11] <LoronzoGrey> no no no [00:00:16] <LoronzoGrey> i'm assuming equal steps in each direction [00:00:18] <SniperChief> the average being one [00:00:29] <SniperChief> that's not where you started [00:00:34] <Reilwin> It also depends on how you define 'zero' [00:00:43] <Reilwin> 'zero' as the number representing nothingness [00:00:45] <LoronzoGrey> i look at numbers as charges [00:00:53] <LoronzoGrey> so zero is the area between positive and negative [00:00:56] <Reilwin> Or 'zero' as a placeholder within a positional number system [00:01:28] <LoronzoGrey> okay [00:01:30] <LoronzoGrey> look [00:01:32] <LoronzoGrey> write 1/0 [00:01:36] <LoronzoGrey> that's infinity [00:01:39] <LoronzoGrey> now [00:01:45] <LoronzoGrey> add 1/0 [00:01:48] <LoronzoGrey> you now have infinity [00:01:51] <LoronzoGrey> plus infinity [00:01:52] <SniperChief> ... [00:01:55] <SniperChief> we've been through this [00:01:57] <LoronzoGrey> 2/0 [00:01:58] <SniperChief> take 0 [00:02:01] <SniperChief> add 0 [00:02:03] <SniperChief> you still have 0 [00:02:08] <LoronzoGrey> no no no [00:02:13] <LoronzoGrey> you don't begin with zero [00:02:15] <LoronzoGrey> you have 2/0 [00:02:21] <LoronzoGrey> and you need to divide by two [00:02:21] <LoronzoGrey> and get [00:02:23] <LoronzoGrey> 2/0 [00:02:25] <LoronzoGrey> which [00:02:27] <LoronzoGrey> is also undefined [00:02:27] <SniperChief> ... [00:02:28] <LoronzoGrey> and infinity [00:02:32] <SniperChief> you haven't divided by 0 [00:02:34] <LoronzoGrey> thus the average of infinity is infinity [00:02:40] <LoronzoGrey> ... [00:02:41] <LoronzoGrey> 1/0 [00:02:42] <Reilwin> LoronzoGrey, SniperChief isn't really using the mathematical definition of infinity [00:02:48] <LoronzoGrey> bah [00:02:55] <SniperChief> what you're doing is the same as saying "take 1/2, then 2/4 - OMG they;re the same thing" [00:02:56] <LoronzoGrey> that's the best way to prove the average [00:02:57] <Reilwin> He's using zero with zero as an arithmetic symbolization of infinity [00:03:10] <Reilwin> it only applies if you use only infinity, of course [00:03:16] <LoronzoGrey> averaging two numbers is an arithmetic action [00:03:24] <LoronzoGrey> arithmetic actions can only be used on numbers [00:03:27] <Reilwin> using other numbers would disrupt the arithmetic [00:03:40] <Reilwin> SniperChief, that's precisely the point [00:03:48] <Reilwin> infinity+infinity = infinity [00:03:51] <Reilwin> same thing [00:03:55] <SniperChief> yes [00:03:58] <SniperChief> I accept that [00:04:04] <Reilwin> multiples of an infinity--are still infinity [00:04:13] <Reilwin> so 1/2 = 2/0 = 3/0 [00:04:15] <Reilwin> oops [00:04:19] <Reilwin> *1/0 [00:04:21] <SniperChief> yes, and multiples of 0 are still 0 :P [00:04:25] <LoronzoGrey> ... [00:04:27] <LoronzoGrey> no [00:04:28] <Reilwin> so 1/0 + 1/0 = 2/0 [00:04:34] <SniperChief> I'm not disputing the facts of infinity [00:04:47] <SniperChief> LoronzoGrey: OK, what coefficient of 0 can you name that doens;t make 0? [00:04:50] <SniperChief> go on [00:04:51] <Reilwin> SniperChief, the main flaw in your substitution of infinity with 0, though [00:05:03] <Reilwin> is this: what happens if you add 1 to 0? [00:05:05] <Reilwin> You get 1 [00:05:07] <Reilwin> that's no longer 0 [00:05:12] <Reilwin> which you use to symbolize infinity [00:05:12] <SniperChief> yes [00:05:16] <SniperChief> no, wait [00:05:27] <LoronzoGrey> haha [00:05:42] <SniperChief> that, in infinity terms, is like having the extra step forward [00:05:48] <LoronzoGrey> but see [00:05:49] <SniperChief> but infinity requires an extra step back [00:05:56] <LoronzoGrey> infinity +1 = infinity [00:05:58] <SniperChief> ergo, still infinity [00:06:05] <SniperChief> because infinity basically regulates itself [00:06:16] <SniperChief> to make sure annoying little +c values don't get in the way ;-) [00:06:21] <LoronzoGrey> pause. [00:06:24] <LoronzoGrey> so sniperchief [00:06:26] <Reilwin> um [00:06:32] <LoronzoGrey> you're seeking to prove: [00:06:40] <Reilwin> are you still applying that to the average of infinity? [00:06:54] <Reilwin> because I was just thinking of the equation: [00:07:01] <Reilwin> infinity + 1 = infinity [00:07:05] <Reilwin> 0 + 1 = 1 [00:07:10] <Reilwin> 1 != infinity [00:07:16] <SniperChief> disnae work [00:07:20] <SniperChief> 0 is *not* infinity [00:07:30] <Reilwin> um...duh... [00:07:34] <LoronzoGrey> haha [00:07:38] <Reilwin> but you've been telling us here [00:07:39] <SniperChief> so you can;t say: [00:07:42] <SniperChief> [00:07] <Reilwin> infinity + 1 = infinity [00:07:42] <SniperChief> [00:07] <Reilwin> 0 + 1 = 1 [00:07:46] <SniperChief> because it's not the same thing [00:07:51] <LoronzoGrey> ... [00:07:58] <Reilwin> that you're using zero to represent infinity [00:08:06] <Reilwin> so, according to your definition [00:08:09] <Reilwin> that's what I did [00:08:15] <Reilwin> used zero to symbolize infinity [00:08:16] <SniperChief> zero represents the ultimate outcome of infinity [00:08:29] <SniperChief> not actually symbolising it [00:08:37] <Reilwin> Could you define 'ultimate outcome' ? [00:08:48] <LoronzoGrey> to assign a positive or negative value to an undefinable concept is presumptuous [00:08:51] <SniperChief> basically, the one step forward, one step back [00:09:12] <SniperChief> not to Reilwin, he says there is a positive and negative infinity :P [00:09:18] <SniperChief> that's what started the whole discussion :-) [00:09:20] <Reilwin> SniperChief, but what if you just have the infinite set of all positive numbers? [00:09:22] <LoronzoGrey> there is [00:09:33] <LoronzoGrey> but see that's -1 (infintity) [00:09:36] <LoronzoGrey> infinity itself [00:09:43] <LoronzoGrey> just is [00:09:51] <LoronzoGrey> thus it's associated with positivity [00:09:59] <LoronzoGrey> infinity the conept [00:10:01] <LoronzoGrey> is positive [00:10:04] <LoronzoGrey> not positive AND negative [00:10:09] <Reilwin> How would you define the ultimate outcome then? [00:10:21] <LoronzoGrey> me? [00:10:28] <SniperChief> hag on, I'm thinking [00:10:52] <Reilwin> and positive infinity is simply a short way of saying [00:11:05] <Reilwin> the set of all positive numbers of the given field [00:11:11] <SniperChief> and LoronzoGrey, using absolutes in this discussion is not the way forward, see creationist debates [00:11:13] <Reilwin> just like negative infinity is a short way of saying [00:11:21] <Reilwin> the set of all negative numbers of the given field [00:12:00] <LoronzoGrey> question [00:12:11] <LoronzoGrey> why do you type out loronzogrey rather than just loronzo? [00:12:25] <LoronzoGrey> just a curiousity that i've noticed everyone does [00:12:27] <SniperChief> I don't [00:12:32] <LoronzoGrey> ? [00:12:33] <SniperChief> I press L + tab [00:12:41] <LoronzoGrey> L [00:12:43] <Reilwin> LoronzoGrey, do you know of tab-completion? [00:12:47] <LoronzoGrey> no i don't [00:12:52] <Reilwin> type the beginning of somebody's name [00:12:57] <Reilwin> enough to make it unique [00:12:58] <LoronzoGrey> Reilwin: who! [00:12:59] <Reilwin> then hit tab [00:13:01] <LoronzoGrey> whoah* [00:13:09] <LoronzoGrey> what if there's two of a letter? [00:13:14] <SniperChief> Reilwin: I suppose I would say that while you stretch infinitely off into positive, the numbers are also stretching infinitely into negative [00:13:25] <SniperChief> now you can say "ah, but that's not happening in this example" [00:13:26] <SniperChief> but [00:13:33] <SniperChief> that's the finite point on the infinite scale [00:13:34] <SniperChief> that is not 0 [00:13:36] <LoronzoGrey> brb [00:13:37] <Reilwin> SniperChief, *does not compute* [00:14:03] <Reilwin> finite on an infinite scale is a false statement [00:14:09] <SniperChief> why? [00:14:20] <SniperChief> 1 is a finite point on the infinite number line [00:14:28] <SniperChief> so is 15,678,986 [00:14:29] <Reilwin> It's impossible for something to be finite-yet infinite-at the same time [00:14:42] <Reilwin> 15,678,986 is finite [00:14:44] <Reilwin> not infinite [00:14:46] <SniperChief> I know [00:14:47] <Reilwin> big number maybe [00:14:49] <SniperChief> but the infinite scale [00:14:51] <Reilwin> but still not infinite [00:14:53] <SniperChief> is made up of finite points [00:14:57] <Reilwin> oops, nv, [00:15:04] * Reilwin reread SniperChief 's statement [00:15:12] <Reilwin> But SniperChief [00:15:19] <Reilwin> if there aren't any negative numbers [00:15:31] <Reilwin> within the set [00:15:39] <Reilwin> how can you say that...there are? [00:16:13] <SniperChief> OK, this is tricky, as I think you;re approaching it from a purely mathematical angle,while I'm taking it from a more philosophocal viewpoint [00:16:38] <LoronzoGrey> yeah i've been thinking completely arithmetically [00:16:40] <Reilwin> heheh, you're right, I'm doing so entirely from the point of view of mathematics [00:16:44] <SniperChief> it's like.... every action has an equal and opposite reaction [00:16:51] <SniperChief> everything has an opposite [00:16:53] <SniperChief> light and dark [00:16:55] <LoronzoGrey> so you're looking at infinity as gaia? [00:16:56] <SniperChief> matter and anti matter [00:17:14] <SniperChief> you can;t say "Oh, I'll add another 10,000 values into the universe, this'll screw with him" [00:17:27] <SniperChief> because at the same time 10,000 going the other way are created [00:17:34] <Reilwin> SniperChief, I thought you said that you didn't accept my idea of positive and negative infinity at first [00:17:40] <SniperChief> or, 0, the starting point, is shifted up [00:17:42] <LoronzoGrey> you do realize that antimatter is a theory [00:17:44] <SniperChief> yes, but you convinced me [00:17:47] <Reilwin> but now it seems you adhere to it strictly [00:17:53] <Reilwin> LoronzoGrey, it is a theory [00:17:58] <LoronzoGrey> as is spontaneous creation [00:17:59] <Reilwin> and it's also true [00:18:03] <LoronzoGrey> so they kind of cancel each other out [00:18:08] <SniperChief> I know, I hadn't thought of it enough, but you were right on that part [00:18:38] <LoronzoGrey> you can't say a theory is true [00:18:44] <Reilwin> LoronzoGrey, a 'theory' is not necessarily an idea without backing [00:18:50] <SniperChief> yo, LoronzoGrey [00:18:54] <Reilwin> LoronzoGrey, but antimatter has been created in the laboratories [00:18:58] <SniperChief> see "philosophical viewpoint" statement [00:19:04] <Reilwin> in tiny, minuscule quantities maybe [00:19:13] <SniperChief> everything we decide is based on assumptions [00:19:18] <SniperChief> strating with the largest one, existence [00:19:19] <Reilwin> but it has still been incontrovertibly proven [00:19:23] <SniperChief> which is a can of worms I'd rather not open [00:19:24] <LoronzoGrey> okay, then it's not theory, it's fact [00:19:33] <LoronzoGrey> oh.. wait [00:19:36] <LoronzoGrey> if it's been created [00:19:38] <LoronzoGrey> how is it not proven [00:19:46] <SniperChief> well, it's been created with matter [00:19:47] * Reilwin hates statements like "It's not a theory, it's a fact" [00:19:47] <LoronzoGrey> wait [00:19:55] <LoronzoGrey> how do you create ANTI matter [00:19:57] <Reilwin> The theory of gravity...is a gravity [00:19:59] * LoronzoGrey is boggled [00:20:14] <Reilwin> LoronzoGrey, by smashing up atoms together really, really fast [00:20:15] <SniperChief> but we don't know that it necessarily comes with matter *all the time* [00:20:19] <Reilwin> See CERN [00:20:30] <SniperChief> it's like going out in th rain [00:20:32] <SniperChief> and getting wet [00:20:36] <Reilwin> and other particle accelerators [00:20:48] <SniperChief> and saying "ah, I'm wet when it rains, I will thereofore *only* be wet when it rains" [00:20:50] <Reilwin> The theory of gravity...is a gravity [00:20:55] <SniperChief> and then get a massive surprise when you;re thrown in a pond :P [00:20:58] <Reilwin> Does that mean that, just because it's a theory [00:21:09] <Reilwin> you'll suddenly fly up in the air at any moment? :P [00:21:26] <SniperChief> homework: prove you exist, using purely objective facts [00:21:26] <LoronzoGrey> in the scope of this discussion i use theory as unproven ideas and fact as proven [00:21:29] <SniperChief> ;-) [00:21:30] <LoronzoGrey> and as far as logic goes [00:21:42] <LoronzoGrey> building on theory is bad [00:21:59] <Reilwin> LoronzoGrey, ok--meh, using the vulgar definition of theory [00:22:06] <SniperChief> antimatter is a fact as much as you [00:22:15] * Reilwin prefers the scientific version, but oh well [00:22:18] <LoronzoGrey> :p [00:22:34] * Reilwin thinks everybody now agrees on the antimatter point [00:22:37] <LoronzoGrey> haha [00:22:42] <Reilwin> back to infinity [00:22:45] <Reilwin> um, where were we? [00:22:46] <SniperChief> anyone feeling particularly debonair and want to post this on the wiki page for IRC quotes? [00:22:46] <SniperChief> :P [00:22:52] <Reilwin> The set of all positive numbers [00:22:55] <LoronzoGrey> haha, not it [00:23:03] <Reilwin> What would the ultimate outcome of that be? [00:23:09] * LoronzoGrey touches his nose with his pointer finger. [00:23:12] <Reilwin> lol, sure :P [00:23:16] <SniperChief> the creation of the set of all negative numbers to balance it [00:23:30] <LoronzoGrey> but see [00:23:31] <Reilwin> hum [00:23:37] <LoronzoGrey> using the idea of equal and opposite [00:23:40] <SniperChief> this is a point we're not going to agree on, I thinl [00:23:42] <LoronzoGrey> creation negates destruction [00:23:44] <Reilwin> I don't think you ever explained how the 'ultimate outcome' was calculated [00:23:57] <Reilwin> wait [00:23:58] <LoronzoGrey> so you can't even have zero as it would have an opposite somehow? [00:24:00] <Reilwin> a step forward [00:24:02] <Reilwin> a step back [00:24:03] <Reilwin> right? [00:24:08] <SniperChief> hm [00:24:09] <SniperChief> well [00:24:15] <SniperChief> it's better to think of t as two people [00:24:21] <LoronzoGrey> ooo [00:24:23] <LoronzoGrey> a duel [00:24:25] <LoronzoGrey> :) [00:24:32] <SniperChief> or, two yous - there's one of you starting at a point on a line [00:24:39] <SniperChief> one of you goes forward, to 1 [00:24:43] <SniperChief> the other goes backwards, to -1 [00:24:59] <Reilwin> SniperChief, the main thing I see in your logic [00:25:03] <SniperChief> you continue doing this, ad infinitum [00:25:05] <Reilwin> Is that it all rests on the assumption [00:25:09] <Reilwin> that you begin at zero [00:25:13] <SniperChief> wait [00:25:15] <SniperChief> let me finish [00:25:16] <Reilwin> What if you don't? [00:25:31] <SniperChief> the distance between them will be equal [00:25:36] <SniperChief> well [00:25:39] <SniperChief> between them and the starting point [00:25:43] <SniperChief> ominally zero [00:26:10] <LoronzoGrey> ominally? [00:26:13] <SniperChief> *nominally [00:26:16] <LoronzoGrey> the displacement is zero [00:26:22] <SniperChief> i.e., I'm using that for simplicits sak,equite wrongly [00:26:24] <SniperChief> yeah [00:26:37] <SniperChief> you could start at 2 [00:26:42] <LoronzoGrey> you're basing this argument not on concrete beginning positon [00:26:44] <LoronzoGrey> but overall change [00:26:45] <LoronzoGrey> i gotcha [00:26:58] <SniperChief> but the difference would take them to move nowhere from that point when you took the distances travelled away form each other [00:27:19] <Reilwin> So basically, if you start at zero [00:27:26] <Reilwin> the 'ultimate outcome' would be zero [00:27:29] <Reilwin> Start at two [00:27:39] <Reilwin> the 'ultimate outcome' would be two [00:27:42] <SniperChief> the only "problem" with using 2 as a strating point is that you might assume the guy moving from 2 oto 1 has travelled 1 [00:27:46] <SniperChief> when he's moved -1 [00:28:01] <Reilwin> SniperChief, we're assuming people do everything right [00:28:06] <LoronzoGrey> Reilwin, SniperChief is simply using a subjective definition [00:28:13] <Reilwin> LoronzoGrey, I know that [00:28:19] <Reilwin> I was getting to that :P [00:28:20] <LoronzoGrey> dispotion is the argument and the beginning point is moot [00:28:32] <Reilwin> Your method as I understand it [00:28:36] <Reilwin> is basically this: [00:28:38] <LoronzoGrey> adding an observer convolutes the argument... [00:28:41] <Reilwin> Take a point, any point [00:28:59] <Reilwin> Take all the numbers going in one direction (infinite) [00:29:10] <Reilwin> Take all the number going in the other direction (infinite) [00:29:14] <LoronzoGrey> no no no [00:29:18] <Reilwin> Subtract their sums [00:29:22] <SniperChief> LoronzoGrey: let him finish [00:29:30] <LoronzoGrey> the fact that you change direction changes it to -1 (infinity) but continue [00:29:30] <SniperChief> Ishould be the one to tell him if he's wrong. I deserve it :P [00:29:42] <SniperChief> er, subtract? [00:29:54] <Reilwin> hum [00:29:56] <LoronzoGrey> you add Reilwin ;) [00:30:00] <SniperChief> you;re using distance, I'm using vectors [00:30:02] <SniperChief> I'd add [00:30:13] <SniperChief> like i + (-i) [00:30:17] <Reilwin> Right, I forgot you were had the negative numbers mean negative [00:30:41] <LoronzoGrey> so you get 0/2 [00:30:45] <LoronzoGrey> 0 [00:31:10] * Reilwin was thinking of the numbers as absolutes going to infinity [00:31:22] <Reilwin> add or subtract though [00:31:27] <Reilwin> it's still infinity + infinity [00:31:30] <SniperChief> this is still "every action has an equal and opposite reaction" [00:31:31] <Reilwin> you get infinity [00:31:37] <Reilwin> but SniperChief [00:31:47] <Reilwin> you're assuming that infinity has an actual, complete value [00:31:53] <SniperChief> every time you slide to the left, you slide to the right, and the midpoint is still where you started [00:31:54] <SniperChief> no [00:31:55] <Reilwin> that can be added to/subtracted from [00:31:58] <SniperChief> absolutely not [00:32:13] <LoronzoGrey> i'm agreeing with SniperChief now... [00:32:21] <SniperChief> I'm not trying to absolutely quantify infinity as a number [00:32:24] <SniperChief> because it's not a number [00:32:32] <Reilwin> but what if you slide left--and stay there? [00:32:33] <LoronzoGrey> for every action taken there is an equal and opposite [00:32:41] <Reilwin> what if there is no 'number' to slide right to? [00:32:43] <SniperChief> then infinity - the *concept* - will make you slide right [00:32:47] <SniperChief> or mae your clone slide right [00:32:52] <LoronzoGrey> that's a fundamental assumption in this argument [00:33:03] <Reilwin> what if the clone has nothing to slide right to? [00:33:10] <SniperChief> then it's not infinity [00:33:14] <Reilwin> What if there's a yawning void into which he falls into? [00:33:14] <SniperChief> you;ve reached the end of infinity [00:33:17] <SniperChief> which justcan;t exist [00:33:23] <LoronzoGrey> exactly, it's not infinity any longer if it terminates [00:33:24] <SniperChief> congratulations [00:33:32] <SniperChief> you;ve destroyed reality by logic :P [00:33:37] <Reilwin> it could also mean you're simply at a 'smaller' infinity [00:33:47] <LoronzoGrey> there is no "smaller" infinity [00:33:50] <SniperChief> explain? [00:33:55] <Reilwin> LoronzoGrey, unfortunately, you're wrong [00:34:02] <Reilwin> for example, the set of all real numbers [00:34:09] <Reilwin> is greater than the set of all natural numbers [00:34:22] <LoronzoGrey> not if neither set continues infinitely [00:34:26] <LoronzoGrey> if you give them the same bounds [00:34:27] <LoronzoGrey> then yes [00:34:30] <LoronzoGrey> but if they're both infinite [00:34:32] <LoronzoGrey> then no [00:34:43] <Reilwin> LoronzoGrey, it's difficult to explain mathematically via IRC [00:34:44] <LoronzoGrey> continuance defeats logic [00:34:48] <Reilwin> but here's how I think of it [00:34:52] <LoronzoGrey> but i understand what you're saying [00:34:55] <Reilwin> all natural numbers are integers [00:34:57] <LoronzoGrey> like in improper integrals [00:35:02] <Reilwin> 1, 2, 4, -1, -100, etc [00:35:05] <Reilwin> however [00:35:14] <Reilwin> real numbers aren't limited to integers [00:35:20] <Reilwin> 1, 1.3, 1.0001, 1.0000000000001 [00:35:29] <Reilwin> within each integer number of the reals [00:35:34] <Reilwin> lies an infinity [00:35:45] <LoronzoGrey> (infinity)^2 over (infinity)^3 would be 0 [00:35:47] <Reilwin> you could think of it as an infinite infinity [00:35:51] <LoronzoGrey> same idea yeah or no? [00:35:59] <Reilwin> LoronzoGrey, it's more like infinity^infinity [00:36:04] <Reilwin> if such a thing could exist [00:36:13] <LoronzoGrey> i know that's what your argument was [00:36:17] <LoronzoGrey> but is it the same logic applied [00:36:20] <Reilwin> um... [00:36:32] <LoronzoGrey> see [00:36:32] <Reilwin> infinity to a power, is definitely the same infinity [00:36:35] <LoronzoGrey> in your example [00:36:42] <Reilwin> but infinity to the power of INFINITY [00:36:47] <Reilwin> Is NOT the same [00:37:01] <LoronzoGrey> natural numbers are infinite when unbounded [00:37:07] <LoronzoGrey> real numbers aren't [00:37:15] <Reilwin> ... [00:37:16] <LoronzoGrey> wait [00:37:18] <LoronzoGrey> i mean [00:37:23] <Reilwin> um, what is your definition of real numbers? [00:37:26] <LoronzoGrey> real numbers are infinite when bounded [00:37:30] <LoronzoGrey> natural are not [00:37:43] <LoronzoGrey> because there are only so many integers [00:37:49] <LoronzoGrey> but real numbers continually get smaller [00:37:59] <LoronzoGrey> which allows you to to travel from a to be [00:38:01] <LoronzoGrey> b* [00:38:07] <LoronzoGrey> constantly halving the distance [00:38:08] <Reilwin> and did I say I was referring to the real numbers as bounded? [00:38:13] <LoronzoGrey> and never reach b [00:38:15] <LoronzoGrey> yes [00:38:18] <LoronzoGrey> you said 1, 2, 3 [00:38:25] <LoronzoGrey> and 1.2, 1.55, etc [00:38:32] <LoronzoGrey> but the fact that you think about it concretely [00:38:35] <LoronzoGrey> implies bounds [00:38:36] <Reilwin> those were examples [00:38:39] <LoronzoGrey> unbounded is unbounded [00:38:50] <Reilwin> If I meant bounded [00:38:55] <Reilwin> I would either have said so [00:38:59] <Reilwin> or typed [00:39:06] <SniperChief> wait a sec [00:39:08] <Reilwin> (1, 1.2, 1.55) [00:39:09] <SniperChief> need to read back [00:39:11] <LoronzoGrey> i'm not saying your agrument explicity invokes a bound [00:39:23] <LoronzoGrey> but that in essence it implies bounds [00:39:26] <LoronzoGrey> look at it like this [00:39:27] <Reilwin> But if you really want me to be explicit, fine [00:39:33] <LoronzoGrey> locusts swarm my fields [00:39:36] <LoronzoGrey> more than i can count [00:39:40] <LoronzoGrey> i can it an infinite amount [00:39:42] <Reilwin> 1, 1.3, 1.0001, *...* [00:39:43] <LoronzoGrey> the next year [00:39:49] <LoronzoGrey> another infinite amount repeat the procdure [00:39:54] <LoronzoGrey> they can be different [00:39:58] <LoronzoGrey> by from my stand point [00:39:59] <LoronzoGrey> both are infinite [00:40:07] <LoronzoGrey> and undefinable [00:40:10] <SniperChief> I'm pretty sure there's a flaw in there [00:40:14] <SniperChief> but it'sa good meta [hor [00:40:19] <SniperChief> and I'll let reilwin take that one [00:40:38] <LoronzoGrey> haha lets see [00:40:41] <LoronzoGrey> now lets say the third year [00:40:44] <LoronzoGrey> each locust [00:40:56] <LoronzoGrey> (this is in our reality impossible, but it's a thought experiment so bear with me) [00:41:04] * Reilwin doesn't understand this sentence: [00:41:08] <Reilwin> <LoronzoGrey> i can it an infinite amount [00:41:15] <SniperChief> he calls it an infinite amount [00:41:27] <LoronzoGrey> oops yeah that's what i meant [00:41:33] <LoronzoGrey> but anyway [00:41:35] <SniperChief> consider his limiting counting ability to be the limitations of the universe [00:41:36] <LoronzoGrey> this third year [00:41:55] <LoronzoGrey> the locusts split into an uncountable mass [00:42:06] <LoronzoGrey> like, each individual of the first mass [00:42:07] <Reilwin> So you're assuming the number of locusts within that year are infinite? [00:42:27] <LoronzoGrey> subjectively [00:43:11] <LoronzoGrey> infinity hinges upon its definability [00:43:12] <SniperChief> btw, I have a rebuttal to the ininifyt size argument once loronzo's done, but oin the meantime I'm gonna air guitar to inspectionwise 1999 [00:43:12] <LoronzoGrey> so thus [00:43:19] <Reilwin> if it's subjectively, I don't understand it [00:43:31] <LoronzoGrey> infinity itself is subjective [00:43:36] <Reilwin> however, if it objectively means there's an infinite number of locusts [00:43:42] <Reilwin> then I would say this: [00:43:44] <LoronzoGrey> objectively [00:43:47] <LoronzoGrey> everything is countable [00:43:52] <Reilwin> the number of locusts in a field, in one year [00:43:54] <LoronzoGrey> objectively everything is defined [00:44:03] <LoronzoGrey> definitions are subjective ;) [00:44:07] <Reilwin> would be comparable to the set of all natural numbers [00:44:18] <LoronzoGrey> right [00:44:26] <LoronzoGrey> and then the third year it's all real numbers [00:44:29] <Reilwin> the number of locusts in a field, for an infinite number of years, would be comparable to the set of all real numbers [00:44:39] <LoronzoGrey> but both are equally infinite to me [00:45:06] <Reilwin> sure, to humans counting, you don't care whether one infinity is greater than the other [00:45:15] <Reilwin> they're both beyond your ability to count [00:45:22] <Reilwin> but to te mathematician [00:45:29] <Reilwin> you're very concerned [00:45:43] <Reilwin> because you can represent infinity as a symbol [00:45:44] <LoronzoGrey> who can count very much higher through his knowledge and notation [00:45:54] <LoronzoGrey> you're simply proving my point of subjectivity [00:46:18] <SniperChief> Reilwin: infinity as a symbol is simply "> you" :P [00:46:25] <Reilwin> SniperChief, :P [00:46:51] <Reilwin> LoronzoGrey, by subjective, I mean something which can vary from human to human, according to beliefs, desires, viewpoints, etc [00:47:00] <SniperChief> OK, so can I launch into my rebuttal? [00:47:03] <Reilwin> by objective, I mean something which remains TRUE, no matter what [00:47:05] <Reilwin> sure [00:47:11] <LoronzoGrey> i don't believe in absolute truths [00:47:17] <LoronzoGrey> everything is my perspective [00:47:19] <LoronzoGrey> ;) [00:47:22] <LoronzoGrey> go SniperChief [00:47:39] <Reilwin> Well, of course, everything viewed through human eyes is subjective [00:47:46] <SniperChief> you;re basically saying because (let's take it as an example) you're counting the different to 6 decimal places, and I'm counting to zero decimal places [00:47:48] <Reilwin> we can't really say that anything we do is objective [00:48:01] <Reilwin> but within the dreamland of theory, we can ;) [00:48:08] <SniperChief> to you go to 0.000001 and I go to 1, if we start from 0 [00:48:25] <SniperChief> your contetion would be that I go to a million and you reach 1 [00:48:37] <LoronzoGrey> yeah [00:48:46] <LoronzoGrey> so what i'm saying is [00:48:50] <SniperChief> and by extension I can go to infinity and you be far, far behind me [00:48:55] <SniperChief> but [00:49:09] <SniperChief> what that simplieifes to, is infinity/finity [00:49:11] <SniperChief> which = infinity [00:49:24] <SniperChief> so I would say that their sizes are still the same [00:49:33] <SniperChief> linking into my point about 0 [00:50:11] <SniperChief> (here, you would have infinity/10^6) [00:50:24] <SniperChief> (while I would have infinity/1) [00:50:42] <LoronzoGrey> haha nice [00:51:46] <Reilwin> hum [00:52:06] <Reilwin> what do you mean when you say the 'size' of an infinity? [00:52:28] <SniperChief> well, it's difficult [00:52:41] <SniperChief> because I think the premise s fundamnetally flawed by the idea of getting *to* infinity [00:52:52] <SniperChief> (...and beyond! as buzz lightyear would say...) [00:53:07] <LoronzoGrey> haha [00:53:19] <LoronzoGrey> instilling faulty ideas in our childrens heads! [00:53:21] <LoronzoGrey> yay [00:53:25] <LoronzoGrey> you know the problem with the US? [00:53:32] <LoronzoGrey> we tell everyone they can be president [00:53:37] <SniperChief> but your infinity is grater than mine because (supposedly) it contains more values [00:53:41] <LoronzoGrey> no they freaking can't. [00:53:47] <SniperChief> and therefore it must be bigger [00:53:51] <SniperChief> that's what I think you;re saying [00:53:57] <SniperChief> I'm trying to disprove that [00:54:01] <LoronzoGrey> SniperChief: when you say that [00:54:06] <LoronzoGrey> you only know from here to there [00:54:12] <LoronzoGrey> that they are disproportionate [00:54:16] <LoronzoGrey> so you're bounding yourself [00:54:17] <SniperChief> I know LoronzoGrey [00:54:21] <Reilwin> SniperChief, that's right, I count the size of the infinities by the number of elements they contain [00:54:24] <LoronzoGrey> which defeats the point of going to infinity [00:54:32] <SniperChief> look, tell Reilwin, it's his point :P [00:54:33] <Reilwin> However, I don't say we actually 'reach' the infinity [00:54:52] <Reilwin> because to do so, you'd need to count infinity using a finite number [00:54:56] <SniperChief> yeah [00:54:56] <Reilwin> clearly an oxymoron [00:55:13] <Reilwin> In order to count infinity, you can only do so using an infinite number ;) [00:55:30] |<-- Innoova has left quakenet (Ping timeout) [00:55:39] <SniperChief> I dub thee Sir Infinite, an thy quest shall be to find the Infinite Number! [00:55:54] <SniperChief> (or *a* one, we're not too fussy at this point) [00:56:00] <SniperChief> :P [00:56:34] <Reilwin> Well, so far, we've been calling the set of all natural numbers to be infinity [00:56:38] <LoronzoGrey> haha [00:56:39] <SniperChief> but I believe my earlier logic should still holdup [00:56:39] <LoronzoGrey> man [00:56:40] <Reilwin> etc [00:56:43] <LoronzoGrey> i'd HATE to be sir infininte [00:56:58] <Reilwin> when what we really mean [00:57:08] <Reilwin> is that the set of all natural numbers [00:57:15] <LoronzoGrey> well i need to go eat [00:57:18] <Reilwin> is a set with an infinite number of elements [00:57:18] <LoronzoGrey> peace men [00:57:23] <Reilwin> Bye, LoronzoGrey ;) [00:57:29] |<-- LoronzoGrey has left quakenet (Quit: ChatZilla 0.9.80 [Firefox 2.0.0.11/2007112718]) [00:58:23] <Reilwin> Ok, remember what I said about the the set of all naturals being equal to the set of all odds, and etc with the set of evens? [00:58:32] <Reilwin> we did so by pairing them up [00:58:44] <Reilwin> and seeing that the set of all natural numbers was used up [00:58:59] <Reilwin> Now, the question is [00:59:10] <Reilwin> Can you pair up the set of all reals with the set of all naturals? [01:00:08] <SniperChief> hmm [01:00:36] <SniperChief> how do you mean pair up? [01:00:52] <Reilwin> Well, for the set of naturals to evens, you could pair them up like so: [01:00:56] <SniperChief> my concern is that here we're diving into the murky area of Zeno's paradoxes [01:01:05] <Reilwin> 2(1st), 4(2nd), 6(3rd), etc [01:01:23] <Reilwin> such that a function f(x) = 2x [01:01:29] <Reilwin> where x is the ordinal number [01:01:32] <SniperChief> (which is, incidentally, where I got my revised ideas of infinity from) [01:01:44] <Reilwin> (heheh,I see) [01:02:15] <Reilwin> in short, to show that the set of all reals is equal to the set of all naturals [01:02:36] <Reilwin> can you construct a function that provides a 1-1 relationship between each other? [01:04:20] <SniperChief> I'm going to duck out of that one by claiming it's 1am :P [01:04:53] <SniperChief> but my problem is still that while the range of infinite reals is a *lot* bigger than the range of infinite naturals [01:05:23] <SniperChief> you're still going to run into n(infinity) = infinit [01:05:41] <SniperChief> where n is however many times bigger the reals are [01:05:58] <Reilwin> You're just ducking out of it by saying that from out perspective, all infinities are the same [01:06:02] <SniperChief> as you said, you can't measure infinity with a finite number [01:06:20] <Reilwin> I'm saying that an infinite which is infinitely larger than an infinity [01:06:28] <Reilwin> is GREATER than that infinity [01:06:30] <SniperChief> oh, now we're going somewhere [01:06:40] <Reilwin> in the only way which makes sense when we consider infinities [01:06:48] <Reilwin> it's infinitely greater than that infinity [01:06:55] <SniperChief> yes, because then n is not a finite number [01:07:15] <Reilwin> ... [01:07:21] <Reilwin> are you agreeing with me or not? [01:07:36] <SniperChief> I'm thinkign [01:07:38] <SniperChief> hang on :P [01:09:11] <Reilwin> lol [01:09:13] <Reilwin> you said that [01:09:21] <Reilwin> not knowing whether you agreed with me or not? :P [01:09:43] <SniperChief> OK, I'm sure there's a flaw in saying infinity^2 is necessarily greater than infinity, but the precise nature of what it is is dancing out of reach [01:09:56] <SniperChief> so I'll agree for now until I can remmeber why I should be disagreeing :P [01:10:45] <Reilwin> SniperChief, I'm not saying that infinity² > infinity [01:10:58] <Reilwin> I'm saying infinity^infinity > infinity [01:11:07] <SniperChief> ... [01:11:30] <SniperChief> right [01:11:55] <SniperChief> my bad [01:12:01] <Reilwin> or is that what I'm saying? [01:12:05] * Reilwin thinks again [01:12:26] <SniperChief> [01:06] <Reilwin> I'm saying that an infinite which is infinitely larger than an infinity [01:12:26] <SniperChief> [01:06] <Reilwin> is GREATER than that infinity [01:12:33] <SniperChief> that's infinity x infinity [01:12:38] <SniperChief> which is infinity² [01:12:42] <Reilwin> which is infinity² [01:12:48] <Reilwin> yeah, that's correct [01:13:44] <Reilwin> and infinity [0,1) + infinity [1, 2) + infinity [2,3) + ... ad infinitum [01:13:50] <Reilwin> equals infinity * infinity [01:13:59] <Reilwin> not infinity^infinity [01:14:02] <Reilwin> my bad, sorry :P [01:14:28] <SniperChief> OK [01:14:33] <Reilwin> <SniperChief> OK, I'm sure there's a flaw in saying infinity^2 is necessarily greater than infinity, but the precise nature of what it is is dancing out of reach [01:14:40] <Reilwin> The flaw you might have in mind [01:14:57] <Reilwin> as that then that implies that there's an infinity³, infinity^4, etc [01:15:23] <Reilwin> and that's precisely what is laid out in Cantor's set theory [01:15:26] <SniperChief> ... [01:15:28] <Reilwin> however [01:15:28] <SniperChief> hey [01:15:32] <SniperChief> remmeber when I said I was 16 [01:15:35] <Reilwin> :P [01:15:39] <SniperChief> and that it was 1am [01:15:47] <Reilwin> oh [01:15:49] <Reilwin> um [01:15:54] <Reilwin> when you said 1am [01:16:00] <SniperChief> I will now give you a third reason for me not to know what it is: [01:16:01] <Reilwin> I thought it was a typo for [01:16:04] <Reilwin> 'lame' [01:16:06] <Reilwin> :P [01:16:09] <SniperChief> I'm trying to do my physics coursework :P [01:16:12] <SniperChief> heheh [01:16:22] * Reilwin uses a font which makes it hard to distinguish letters :P [01:16:51] <Reilwin> The interesting thing though [01:16:57] <Reilwin> Is then this: [01:17:06] <Reilwin> Is it possible to have infinity^infinity? [01:17:18] <Reilwin> That is, to have a set which contains all sets--including itself? [01:17:42] * SniperChief is thinking we've drifted from the roiginal and as yet unresolved point [01:18:02] <Reilwin> true, I forgot what the original point was [01:18:03] <Reilwin> do you? [01:18:08] <Reilwin> (remember, that is) [01:18:30] <SniperChief> sizes of infinity [01:19:01] <SniperChief> hang on [01:19:04] <SniperChief> looking for my point [01:20:07] <SniperChief> [00:48:08] <SniperChief> to you go to 0.000001 and I go to 1, if we start from 0 [01:20:07] <SniperChief> [00:48:25] <SniperChief> your contention would be that I go to a million and you reach 1 [01:20:07] <SniperChief> [00:48:50] <SniperChief> and by extension I can go to infinity and you be far, far behind me [01:20:07] <SniperChief> [00:48:55] <SniperChief> but [01:20:07] <SniperChief> [00:49:09] <SniperChief> what that simplifies to, is infinity/finity [01:20:07] <SniperChief> [00:49:11] <SniperChief> which = infinity [01:20:07] <SniperChief> [00:49:24] <SniperChief> so I would say that their sizes are still the same [01:20:07] <SniperChief> [00:49:33] <SniperChief> linking into my point about 0 [01:20:07] <SniperChief> [00:50:11] <SniperChief> (here, you would have infinity/10^6) [01:20:07] <SniperChief> [00:50:24] <SniperChief> (while I would have infinity/1) [01:20:52] <Reilwin> SniperChief, the main problem with that argument [01:21:04] <Reilwin> is that you were looking at the absolute values of the numbers involved [01:21:08] <SniperChief> yeah [01:21:14] <Reilwin> rather than the amount of numbers counted [01:22:56] <SniperChief> OK, do you want to divide infinity by infinity? [01:23:11] <SniperChief> to get 1, while whatever number I use will divide out to infinity? [01:23:31] <SniperChief> cuz that problem would be resolved with the 0 value [01:23:39] <SniperChief> but I'm really having trouble grabbing my thought trains [01:23:51] <SniperChief> and rational debate is rapidly escaping me [01:24:00] <Reilwin> dividing infinity by infinity to equal one [01:24:02] <Reilwin> is only valid [01:24:07] <Reilwin> if you have the same infinity [01:24:14] <SniperChief> eugh [01:24:15] <Reilwin> but sure, let's assume it's the same infinity [01:24:46] <SniperChief> I think I'll be a lot better off with the philosophical "infinity is infinity is infinity" approach :P [01:24:52] <Reilwin> :P [01:24:57] <Reilwin> shore [01:25:20] <Reilwin> but if you ever take calculus, limits, and the limits of polynomial functions [01:25:27] <Reilwin> just remember what I said about infinity :P [01:26:13] <SniperChief> since "actual" infinity is, by definition, something that just can't be counted [01:26:41] <SniperChief> I think we're engaging in a highly advanced "my potential infinity is bigger than your potential infinity" argument :P [01:27:01] <Reilwin> heheh, using Aristotelian terms I see [01:27:14] <Reilwin> the point isn't that it can't be counted though [01:27:27] <Reilwin> because saying that limits it to human, finite counting [01:27:32] <Kel> You guys [01:27:34] <Kel> Are [01:27:35] <Kel> Weird [01:27:37] <Kel> Yet [01:27:39] <Kel> Wonderful [01:27:41] <Reilwin> in short, it's just saying: I don't understand infinity, I don't wanna try [01:27:45] <Reilwin> lol [01:27:57] <Reilwin> you actually went and read through all that, Kel ? o.O [01:28:04] * SniperChief stands by his "mathematicians are going to destroy the universe through logic" statement [01:28:04] <Kel> I skimmed it [01:28:13] <SniperChief> I do want to try [01:28:25] <Reilwin> SniperChief, actually, mathematicians might actually have destroyed mathematics [01:28:27] <SniperChief> and I think I have a much easier, better, simpler and quite possibly wronger answer :P [01:28:41] <Reilwin> Godel's Incompleteness Theorem proved [01:28:50] <Reilwin> that you can prove mathematics to be consistent [01:28:50] <SniperChief> shh [01:28:52] <Reilwin> *can't [01:28:56] <SniperChief> don't tell anyone ;-) [01:29:00] <Reilwin> :P [01:29:22] <SniperChief> eh, but you can't prove the universe to be consistent [01:29:41] <SniperChief> all things are subjective and that [01:29:54] <Reilwin> SniperChief, the difference is [01:30:02] <SniperChief> the onus of proof lies on the accuser to prove that mathematics is *inconsistent* [01:30:03] <Reilwin> you can't prove the universe to be logical either [01:30:14] <GEP> mmm chaos [01:30:18] <Reilwin> SniperChief, the problem is [01:30:39] <Reilwin> you can't prove that mathematics (or any other complicated system of logic) to be consistent OR inconsistent [01:30:44] <SniperChief> the problem is existence. The layout sucks and there's a monopoly on it. Up theological apple! [01:30:53] <SniperChief> ;-) [01:31:01] <Reilwin> :) [01:31:18] <SniperChief> I'll have to look up the theorem just to piss off some teachers [01:32:13] <Reilwin> lol :P [01:32:38] <Reilwin> it's a bit complicated though [01:32:44] <Reilwin> you can prove that, for example [01:33:06] <Reilwin> a certain theory is consistent, in relationship to another [01:33:21] <Reilwin> and finally boil it down to whether or not arithmetics is consistent [01:33:23] <Reilwin> hum [01:33:27] <Reilwin> I think it was arithmetics [01:33:43] <Reilwin> should recheck my notes on that [01:34:08] <Reilwin> in any case, it was proven that the consistency of a large portion of mathematics [01:34:18] <Reilwin> could be reduced to the consistency of a small portion of it [01:34:39] <Reilwin> which means that the consistency of that large portion [01:34:47] <Reilwin> is dependent on the consistency of the small one [01:34:56] <Reilwin> if the small one is inconsistent, so is all the rest [01:35:06] <Reilwin> yadayadayada [01:35:18] <Reilwin> I'll let ye be to your physics homework now :P -- [02:24:46] <SniperChief> d'you know [02:24:49] <SniperChief> it's like 20 odd pages [02:24:55] <SniperChief> and I think we actually didnlt agree on much at all :P