Re: hehe, Infinity


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Re: hehe, Infinity

Posted By: treellama Date: 12/15/06 12:18 p.m.
In Response To: Re: hehe, Infinity (Forrest of B.org)

: Hmm... I remember that the set of all integers and the set of all rationals
: were supposedly the same size, though I was never thoroughly convinced by
: the supposed proof of that.
You can count rational numbers, the same as you can count natural numbers, just have to do it in the right order:
1/1, 1/2, 2/1, 3/1, 2/2, 1/3, 1/4, 2/3, 3/2, 4/1, 5/1, etc.
: I'm pretty sure the set of reals is larger
: than either of those, but it may not be the next-largest set; I don't
: think there's consensus on what set is of cardinality aleph-one, only that
: the set of all integers is of cardinality aleph-null.
The set of reals is certainly bigger, because it contains the set of irrational numbers, which are uncountable. I don't think there's a way to prove that the set of reals has cardinality aleph one, but you can make a cardinality aleph one set by taking the set of all possible subsets of a cardinality aleph null set; so, the set of all subsets of natural numbers, would have cardinality 2^aleph null, which is equal to aleph one. I think, lol. I'm really not convinced why any of this is useful, aside from making the brain hurt.

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Pre-2004 Posts

Replies:

The Garden of Forking Paths Document 11/29/06 8:50 p.m.

Re: The Garden of Forking Paths Forrest of B.org 11/29/06 10:11 p.m.

*sniff* Duality *sniff *NM* treellama 11/30/06 2:51 a.m.

That's not fair. RyokoTK 11/30/06 5:26 a.m.

Re: That's not fair. McNutcase 11/30/06 5:40 a.m.

Re: That's not fair. RyokoTK 11/30/06 8:51 a.m.

Re: That's not fair. McNutcase 11/30/06 9:25 a.m.

Re: That's not fair. RyokoTK 11/30/06 9:59 a.m.

Re: That's not fair. D-M.A. 11/30/06 10:05 a.m.

Re: That's not fair. RyokoTK 11/30/06 10:22 a.m.

Ahaa, I see what you mean now, point taken. *NM* D-M.A. 11/30/06 10:33 a.m.

define "well" MrHen 11/30/06 10:24 a.m.

Re: define "well" RyokoTK 11/30/06 11:31 a.m.

Re: define "well" Aaron Sikes 11/30/06 12:19 p.m.

Re: define "well" Forrest of B.org 11/30/06 1:26 p.m.

Re: define "well" Aaron Sikes 12/1/06 6:01 a.m.

Mmm... House of Leaves MrHen 11/30/06 8:00 a.m.

Re: The Garden of Forking Paths Vid Boi 11/30/06 8:13 a.m.

Re: The Garden of Forking Paths sdwoodchuck 11/30/06 12:39 p.m.

So, what was your conclusion? *NM* Frungi 11/30/06 3:57 p.m.

Re: So, what was your conclusion? sdwoodchuck 11/30/06 6:18 p.m.

in your theory, the dreams... MrHen 12/1/06 4:44 a.m.

Re: in your theory, the dreams... thermoplyae 12/1/06 6:42 a.m.

Re: So, what was your conclusion? Frungi 12/4/06 6:31 p.m.

Re: So, what was your conclusion? Forrest of B.org 12/4/06 9:07 p.m.

Time Travel and the Psychology of Gods Forrest of B.org 12/4/06 9:25 p.m.

Re: Time Travel and the Psychology of Gods Frungi 12/5/06 8:46 a.m.

Re: Time Travel and the Psychology of Gods Forrest of B.org 12/5/06 4:29 p.m.

heck, I would buy 'em MrHen 12/5/06 6:39 p.m.

Philosophy anyone? Icarus 12/6/06 8:29 a.m.

Re: Philosophy anyone? Forrest of B.org 12/6/06 10:46 a.m.

Re: The Garden of Forking Paths *LINK* Hamish Sinclair 12/2/06 5:06 a.m.

Re: The Garden of Forking Paths Document 12/2/06 6:17 p.m.

Re: The Garden of Forking Paths Document 12/4/06 7:03 p.m.

Official Bungie Canon? Shoeless 12/7/06 7:00 a.m.

Re: Official Bungie Canon? Bob-B-Q 12/7/06 10:14 a.m.

Define "all" MrHen 12/7/06 10:20 a.m.

Re: Define "all" Document 12/7/06 4:20 p.m.

Re: Define "all" Document 12/7/06 4:21 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/11/06 10:28 a.m.

Re: Official Bungie Canon? Shoeless 12/11/06 12:00 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/11/06 12:03 p.m.

Re: Official Bungie Canon? MrHen 12/11/06 1:45 p.m.

Re: Official Bungie Canon? *LINK* Frungi 12/11/06 3:22 p.m.

uh, thanks... MrHen 12/11/06 6:01 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/11/06 9:44 p.m.

I like being confused... MrHen 12/12/06 5:13 a.m.

Re: I like being confused... Forrest of B.org 12/12/06 3:53 p.m.

Re: I like being confused... Frungi 12/12/06 5:51 p.m.

Re: I like being confused... Forrest of B.org 12/12/06 9:42 p.m.

timelines and their glory MrHen 12/13/06 5:14 a.m.

Re: timelines and their glory Forrest of B.org 12/13/06 8:05 a.m.

Mmm... trippy... MrHen 12/13/06 8:20 a.m.

Re: timelines and their glory Frungi 12/13/06 1:43 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/12/06 12:37 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/12/06 4:02 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/12/06 4:43 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/12/06 9:52 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/13/06 4:17 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/13/06 6:06 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/16/06 5:42 p.m.

what? why? MrHen 12/16/06 5:47 p.m.

Re: Official Bungie Canon? kyjel 12/16/06 6:40 p.m.

Re: Official Bungie Canon? Shoeless 12/17/06 4:13 p.m.

Re: Official Bungie Canon? Frungi 12/18/06 5:09 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/18/06 8:47 p.m.

Re: Official Bungie Canon? Frungi 12/18/06 9:22 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/22/06 9:58 a.m.

questions and answers MrHen 12/22/06 12:44 p.m.

Re: Official Bungie Canon? Shoeless 12/22/06 1:24 p.m.

Re: Official Bungie Canon? Shoeless 12/18/06 10:21 p.m.

rabbit trail, sorry... MrHen 12/13/06 5:23 a.m.

Re: rabbit trail, sorry... Chris Biberstein 12/13/06 4:29 p.m.

and the problem was... where? MrHen 12/13/06 7:06 p.m.

Re: and the problem was... where? Forrest of B.org 12/13/06 9:13 p.m.

ah, my bad. I understand. :) *NM* MrHen 12/14/06 4:54 a.m.

Re: ah, my bad. I understand. :) Forrest of B.org 12/14/06 1:22 p.m.

I am the same way. ;) MrHen 12/15/06 5:18 a.m.

Re: I am the same way. ;) Forrest of B.org 12/15/06 7:27 a.m.

Branching MrHen 12/15/06 9:46 a.m.

Re: Branching Forrest of B.org 12/15/06 11:04 a.m.

Actually, I think I did understand. MrHen 12/15/06 4:32 p.m.

Re: Actually, I think I did understand. Forrest of B.org 12/17/06 11:55 a.m.

Oh, okay, then we do disagree. MrHen 12/17/06 6:50 p.m.

Re: Oh, okay, then we do disagree. Forrest of B.org 12/17/06 10:08 p.m.

so where do you get hyper-time? MrHen 12/18/06 5:13 a.m.

Re: so where do you get hyper-time? Forrest of B.org 12/18/06 8:20 a.m.

whoops... no... that is not what I meant. MrHen 12/18/06 9:49 a.m.

Re: whoops... no... that is not what I meant. Forrest of B.org 12/18/06 1:58 p.m.

right, yeah, that is the identity problem MrHen 12/18/06 4:41 p.m.

Re: right, yeah, that is the identity problem Forrest of B.org 12/18/06 9:55 p.m.

ohhh... MrHen 12/19/06 5:44 a.m.

Re: ohhh... Forrest of B.org 12/19/06 9:20 a.m.

back to the math ;) MrHen 12/19/06 11:07 a.m.

Re: back to the math ;) Forrest of B.org 12/19/06 1:36 p.m.

wait, so my model is too... real? ;) MrHen 12/22/06 1:57 p.m.

Sort of. Forrest of B.org 12/22/06 3:22 p.m.

and the light turns on... MrHen 1/7/07 4:41 p.m.

Re: and the light turns on... Forrest of B.org 1/8/07 8:12 p.m.

Re: Official Bungie Canon? Shoeless 12/13/06 8:11 a.m.

Re: Official Bungie Canon? Chris Biberstein 12/13/06 4:34 p.m.

Re: Official Bungie Canon? Shoeless 12/14/06 8:01 a.m.

Re: Official Bungie Canon? Frungi 12/15/06 8:02 a.m.

Re: Official Bungie Canon? Forrest of B.org 12/15/06 8:51 a.m.

Re: Official Bungie Canon? Frungi 12/15/06 9:22 a.m.

hehe, Infinity MrHen 12/15/06 9:51 a.m.

Re: hehe, Infinity Forrest of B.org 12/15/06 11:16 a.m.

Re: hehe, Infinity treellama 12/15/06 12:18 p.m.

Re: hehe, Infinity Forrest of B.org 12/15/06 1:15 p.m.

Re: hehe, Infinity treellama 12/15/06 2:09 p.m.

Re: hehe, Infinity Forrest of B.org 12/15/06 3:15 p.m.

Re: hehe, Infinity treellama 12/15/06 4:12 p.m.

Re: hehe, Infinity Frungi 12/15/06 6:34 p.m.

Re: hehe, Infinity treellama 12/16/06 3:38 a.m.

So... do I have this right? MrHen 12/16/06 6:35 a.m.

Re: So... do I have this right? treellama 12/16/06 11:25 a.m.

Re: hehe, Infinity treellama 12/15/06 2:21 p.m.

Re: Official Bungie Canon? treellama 12/15/06 9:55 a.m.

Re: Official Bungie Canon? McNutcase 12/15/06 11:12 a.m.

Re: Official Bungie Canon? Forrest of B.org 12/15/06 1:20 p.m.

Re: Official Bungie Canon? McNutcase 12/15/06 9:32 a.m.

Re: Official Bungie Canon? MrHen 12/15/06 9:49 a.m.

Re: Official Bungie Canon? treellama 12/15/06 9:56 a.m.

Re: Official Bungie Canon? McNutcase 12/15/06 11:09 a.m.

Re: Official Bungie Canon? Forrest of B.org 12/15/06 1:34 p.m.

Re: Official Bungie Canon? Forrest of B.org 12/15/06 1:39 p.m.

Re: Official Bungie Canon? ukimalefu 12/15/06 6:29 p.m.

Re: Official Bungie Canon? McNutcase 12/15/06 10:23 p.m.

awesome, thanks! *NM* MrHen 12/16/06 6:49 a.m.

Re: Official Bungie Canon? Chris Biberstein 12/16/06 5:51 p.m.

Re: Official Bungie Canon? kyjel 12/16/06 7:08 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/18/06 8:36 p.m.

Re: Official Bungie Canon? Frungi 12/18/06 9:48 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/22/06 10:00 a.m.

Re: Official Bungie Canon? Forrest of B.org 12/22/06 10:19 a.m.

what he said MrHen 12/22/06 12:38 p.m.

Re: Official Bungie Canon? Shoeless 12/18/06 10:23 p.m.

*sigh* MrHen 12/17/06 5:08 a.m.

Re: Official Bungie Canon? Frungi 12/11/06 3:35 p.m.

Re: Official Bungie Canon? Chris Biberstein 12/12/06 12:23 p.m.

Re: Official Bungie Canon? Shoeless 12/13/06 7:56 a.m.

Re: Official Bungie Canon? Forrest of B.org 12/13/06 8:32 a.m.

another example (albeit overused) MrHen 12/13/06 8:57 a.m.

Re: The Garden of Forking Paths *LINK* irons 2/23/18 1:11 a.m.

LOKE *NM* W'rkncacnter 2/23/18 4:06 p.m.

Re: LOKE *NM* *LINK* irons 2/23/18 4:14 p.m.

LOKE *NM* *NM* *NM* *NM* *NM* *LINK* W'rkncacnter 2/23/18 11:09 p.m.

Re: LOKE *NM* *LINK* irons 2/24/18 3:31 a.m.

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Pre-2004 Posts

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: You can count rational numbers, the same as you can count natural numbers, : just have to do it in the right order: 1/1, 1/2, 2/1, 3/1, 2/2, 1/3, 1/4, : 2/3, 3/2, 4/1, 5/1, etc. : The set of reals is certainly bigger, because it contains the set of : irrational numbers, which are uncountable. I don't think there's a way to : prove that the set of reals has cardinality aleph one, but you can make a : cardinality aleph one set by taking the set of all possible subsets of a : cardinality aleph null set; so, the set of all subsets of natural numbers, : would have cardinality 2^aleph null, which is equal to aleph one. I think, : lol. I'm really not convinced why any of this is useful, aside from making : the brain hurt.

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The Garden of Forking Paths	Document	11/29/06 8:50 p.m.
Re: The Garden of Forking Paths	Forrest of B.org	11/29/06 10:11 p.m.
sniff Duality sniff NM*	treellama	11/30/06 2:51 a.m.
That's not fair.	RyokoTK	11/30/06 5:26 a.m.
Re: That's not fair.	McNutcase	11/30/06 5:40 a.m.
Re: That's not fair.	RyokoTK	11/30/06 8:51 a.m.
Re: That's not fair.	McNutcase	11/30/06 9:25 a.m.
Re: That's not fair.	RyokoTK	11/30/06 9:59 a.m.
Re: That's not fair.	D-M.A.	11/30/06 10:05 a.m.
Re: That's not fair.	RyokoTK	11/30/06 10:22 a.m.
Ahaa, I see what you mean now, point taken. NM	D-M.A.	11/30/06 10:33 a.m.
define "well"	MrHen	11/30/06 10:24 a.m.
Re: define "well"	RyokoTK	11/30/06 11:31 a.m.
Re: define "well"	Aaron Sikes	11/30/06 12:19 p.m.
Re: define "well"	Forrest of B.org	11/30/06 1:26 p.m.
Re: define "well"	Aaron Sikes	12/1/06 6:01 a.m.
Mmm... House of Leaves	MrHen	11/30/06 8:00 a.m.
Re: The Garden of Forking Paths	Vid Boi	11/30/06 8:13 a.m.
Re: The Garden of Forking Paths	sdwoodchuck	11/30/06 12:39 p.m.
So, what was your conclusion? NM	Frungi	11/30/06 3:57 p.m.
Re: So, what was your conclusion?	sdwoodchuck	11/30/06 6:18 p.m.
in your theory, the dreams...	MrHen	12/1/06 4:44 a.m.
Re: in your theory, the dreams...	thermoplyae	12/1/06 6:42 a.m.
Re: So, what was your conclusion?	Frungi	12/4/06 6:31 p.m.
Re: So, what was your conclusion?	Forrest of B.org	12/4/06 9:07 p.m.
Time Travel and the Psychology of Gods	Forrest of B.org	12/4/06 9:25 p.m.
Re: Time Travel and the Psychology of Gods	Frungi	12/5/06 8:46 a.m.
Re: Time Travel and the Psychology of Gods	Forrest of B.org	12/5/06 4:29 p.m.
heck, I would buy 'em	MrHen	12/5/06 6:39 p.m.
Philosophy anyone?	Icarus	12/6/06 8:29 a.m.
Re: Philosophy anyone?	Forrest of B.org	12/6/06 10:46 a.m.
Re: The Garden of Forking Paths LINK	Hamish Sinclair	12/2/06 5:06 a.m.
Re: The Garden of Forking Paths	Document	12/2/06 6:17 p.m.
Re: The Garden of Forking Paths	Document	12/4/06 7:03 p.m.
Official Bungie Canon?	Shoeless	12/7/06 7:00 a.m.
Re: Official Bungie Canon?	Bob-B-Q	12/7/06 10:14 a.m.
Define "all"	MrHen	12/7/06 10:20 a.m.
Re: Define "all"	Document	12/7/06 4:20 p.m.
Re: Define "all"	Document	12/7/06 4:21 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/11/06 10:28 a.m.
Re: Official Bungie Canon?	Shoeless	12/11/06 12:00 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/11/06 12:03 p.m.
Re: Official Bungie Canon?	MrHen	12/11/06 1:45 p.m.
Re: Official Bungie Canon? LINK	Frungi	12/11/06 3:22 p.m.
uh, thanks...	MrHen	12/11/06 6:01 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/11/06 9:44 p.m.
I like being confused...	MrHen	12/12/06 5:13 a.m.
Re: I like being confused...	Forrest of B.org	12/12/06 3:53 p.m.
Re: I like being confused...	Frungi	12/12/06 5:51 p.m.
Re: I like being confused...	Forrest of B.org	12/12/06 9:42 p.m.
timelines and their glory	MrHen	12/13/06 5:14 a.m.
Re: timelines and their glory	Forrest of B.org	12/13/06 8:05 a.m.
Mmm... trippy...	MrHen	12/13/06 8:20 a.m.
Re: timelines and their glory	Frungi	12/13/06 1:43 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/12/06 12:37 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/12/06 4:02 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/12/06 4:43 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/12/06 9:52 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/13/06 4:17 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/13/06 6:06 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/16/06 5:42 p.m.
what? why?	MrHen	12/16/06 5:47 p.m.
Re: Official Bungie Canon?	kyjel	12/16/06 6:40 p.m.
Re: Official Bungie Canon?	Shoeless	12/17/06 4:13 p.m.
Re: Official Bungie Canon?	Frungi	12/18/06 5:09 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/18/06 8:47 p.m.
Re: Official Bungie Canon?	Frungi	12/18/06 9:22 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/22/06 9:58 a.m.
questions and answers	MrHen	12/22/06 12:44 p.m.
Re: Official Bungie Canon?	Shoeless	12/22/06 1:24 p.m.
Re: Official Bungie Canon?	Shoeless	12/18/06 10:21 p.m.
rabbit trail, sorry...	MrHen	12/13/06 5:23 a.m.
Re: rabbit trail, sorry...	Chris Biberstein	12/13/06 4:29 p.m.
and the problem was... where?	MrHen	12/13/06 7:06 p.m.
Re: and the problem was... where?	Forrest of B.org	12/13/06 9:13 p.m.
ah, my bad. I understand. :) NM	MrHen	12/14/06 4:54 a.m.
Re: ah, my bad. I understand. :)	Forrest of B.org	12/14/06 1:22 p.m.
I am the same way. ;)	MrHen	12/15/06 5:18 a.m.
Re: I am the same way. ;)	Forrest of B.org	12/15/06 7:27 a.m.
Branching	MrHen	12/15/06 9:46 a.m.
Re: Branching	Forrest of B.org	12/15/06 11:04 a.m.
Actually, I think I did understand.	MrHen	12/15/06 4:32 p.m.
Re: Actually, I think I did understand.	Forrest of B.org	12/17/06 11:55 a.m.
Oh, okay, then we do disagree.	MrHen	12/17/06 6:50 p.m.
Re: Oh, okay, then we do disagree.	Forrest of B.org	12/17/06 10:08 p.m.
so where do you get hyper-time?	MrHen	12/18/06 5:13 a.m.
Re: so where do you get hyper-time?	Forrest of B.org	12/18/06 8:20 a.m.
whoops... no... that is not what I meant.	MrHen	12/18/06 9:49 a.m.
Re: whoops... no... that is not what I meant.	Forrest of B.org	12/18/06 1:58 p.m.
right, yeah, that is the identity problem	MrHen	12/18/06 4:41 p.m.
Re: right, yeah, that is the identity problem	Forrest of B.org	12/18/06 9:55 p.m.
ohhh...	MrHen	12/19/06 5:44 a.m.
Re: ohhh...	Forrest of B.org	12/19/06 9:20 a.m.
back to the math ;)	MrHen	12/19/06 11:07 a.m.
Re: back to the math ;)	Forrest of B.org	12/19/06 1:36 p.m.
wait, so my model is too... real? ;)	MrHen	12/22/06 1:57 p.m.
Sort of.	Forrest of B.org	12/22/06 3:22 p.m.
and the light turns on...	MrHen	1/7/07 4:41 p.m.
Re: and the light turns on...	Forrest of B.org	1/8/07 8:12 p.m.
Re: Official Bungie Canon?	Shoeless	12/13/06 8:11 a.m.
Re: Official Bungie Canon?	Chris Biberstein	12/13/06 4:34 p.m.
Re: Official Bungie Canon?	Shoeless	12/14/06 8:01 a.m.
Re: Official Bungie Canon?	Frungi	12/15/06 8:02 a.m.
Re: Official Bungie Canon?	Forrest of B.org	12/15/06 8:51 a.m.
Re: Official Bungie Canon?	Frungi	12/15/06 9:22 a.m.
hehe, Infinity	MrHen	12/15/06 9:51 a.m.
Re: hehe, Infinity	Forrest of B.org	12/15/06 11:16 a.m.
Re: hehe, Infinity	treellama	12/15/06 12:18 p.m.
Re: hehe, Infinity	Forrest of B.org	12/15/06 1:15 p.m.
Re: hehe, Infinity	treellama	12/15/06 2:09 p.m.
Re: hehe, Infinity	Forrest of B.org	12/15/06 3:15 p.m.
Re: hehe, Infinity	treellama	12/15/06 4:12 p.m.
Re: hehe, Infinity	Frungi	12/15/06 6:34 p.m.
Re: hehe, Infinity	treellama	12/16/06 3:38 a.m.
So... do I have this right?	MrHen	12/16/06 6:35 a.m.
Re: So... do I have this right?	treellama	12/16/06 11:25 a.m.
Re: hehe, Infinity	treellama	12/15/06 2:21 p.m.
Re: Official Bungie Canon?	treellama	12/15/06 9:55 a.m.
Re: Official Bungie Canon?	McNutcase	12/15/06 11:12 a.m.
Re: Official Bungie Canon?	Forrest of B.org	12/15/06 1:20 p.m.
Re: Official Bungie Canon?	McNutcase	12/15/06 9:32 a.m.
Re: Official Bungie Canon?	MrHen	12/15/06 9:49 a.m.
Re: Official Bungie Canon?	treellama	12/15/06 9:56 a.m.
Re: Official Bungie Canon?	McNutcase	12/15/06 11:09 a.m.
Re: Official Bungie Canon?	Forrest of B.org	12/15/06 1:34 p.m.
Re: Official Bungie Canon?	Forrest of B.org	12/15/06 1:39 p.m.
Re: Official Bungie Canon?	ukimalefu	12/15/06 6:29 p.m.
Re: Official Bungie Canon?	McNutcase	12/15/06 10:23 p.m.
awesome, thanks! NM	MrHen	12/16/06 6:49 a.m.
Re: Official Bungie Canon?	Chris Biberstein	12/16/06 5:51 p.m.
Re: Official Bungie Canon?	kyjel	12/16/06 7:08 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/18/06 8:36 p.m.
Re: Official Bungie Canon?	Frungi	12/18/06 9:48 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/22/06 10:00 a.m.
Re: Official Bungie Canon?	Forrest of B.org	12/22/06 10:19 a.m.
what he said	MrHen	12/22/06 12:38 p.m.
Re: Official Bungie Canon?	Shoeless	12/18/06 10:23 p.m.
sigh	MrHen	12/17/06 5:08 a.m.
Re: Official Bungie Canon?	Frungi	12/11/06 3:35 p.m.
Re: Official Bungie Canon?	Chris Biberstein	12/12/06 12:23 p.m.
Re: Official Bungie Canon?	Shoeless	12/13/06 7:56 a.m.
Re: Official Bungie Canon?	Forrest of B.org	12/13/06 8:32 a.m.
another example (albeit overused)	MrHen	12/13/06 8:57 a.m.
Re: The Garden of Forking Paths LINK	irons	2/23/18 1:11 a.m.
LOKE NM	W'rkncacnter	2/23/18 4:06 p.m.
Re: LOKE NM LINK	irons	2/23/18 4:14 p.m.
LOKE NM NM NM NM NM LINK	W'rkncacnter	2/23/18 11:09 p.m.
Re: LOKE NM LINK	irons	2/24/18 3:31 a.m.



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	Message: : You can count rational numbers, the same as you can count natural numbers, : just have to do it in the right order: 1/1, 1/2, 2/1, 3/1, 2/2, 1/3, 1/4, : 2/3, 3/2, 4/1, 5/1, etc. : The set of reals is certainly bigger, because it contains the set of : irrational numbers, which are uncountable. I don't think there's a way to : prove that the set of reals has cardinality aleph one, but you can make a : cardinality aleph one set by taking the set of all possible subsets of a : cardinality aleph null set; so, the set of all subsets of natural numbers, : would have cardinality 2^aleph null, which is equal to aleph one. I think, : lol. I'm really not convinced why any of this is useful, aside from making : the brain hurt.
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