IRC/Quotes/Infinity

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 :-)

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[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