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 contain rambling, nonsense, and dangerously close 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