From the desk of Mitt Romney:
Pages
Author  Topic: From the desk of Mitt Romney: 

...b10010b...
Member # 869

written Friday, February 24 2006 23:34
Profile
Homepage
quote:Consider yourself corrected. Limbo was never an official doctrine of the Catholic Church. It's fallen into disfavour in recent times, and it's widely expected that the current Pope will declare that limbo does not exist and that unbaptised infants go to heaven. quote:Were you told this by a mathematician? If not, take it with a grain of salt. "Infinity" is not a single clearlydefined mathematical concept. [ Friday, February 24, 2006 23:38: Message edited by: Thuryl ]  The Empire Always Loses: This Time For Sure! Posts: 9973  Registered: Saturday, March 30 2002 08:00 
Off With Their Heads
Member # 4045

written Saturday, February 25 2006 07:17
Profile
Homepage
There are greater and lesser infinities that show up in math sometimes.  Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968  Registered: Saturday, February 28 2004 08:00 
Law Bringer
Member # 335

written Saturday, February 25 2006 10:55
Profile
Homepage
But sometimes two that seem like they shouldn't be the same size are the same size even when they obviously can't be. —Alorael, whose infinity is bigger than twice your infinity plus infinity. Posts: 14579  Registered: Saturday, December 1 2001 08:00 
Guardian
Member # 6670

written Saturday, February 25 2006 13:19
Profile
Homepage
Is Limbo the same as Purgatory? Don't we all love the doctrine of the RCC. Need to build a cathedral in Rome. No problem: make the masses think they have to pay their way out of Purgatory. Cod discovered in the Grand Banks? Make it official canon to eat fish on Friday. On infinity: yes, there is more than one infinity. Infinity as expressed by the Reals is infinitely more infinite than infinity as expressed by the Rationals (say that three times fast). If that didn't blow your mind, look here! EDIT: Made the above slightly more understandable.  It is a miracle that curiosity survives formal education.  Albert Einstein [ Saturday, February 25, 2006 13:23: Message edited by: Dintiradan ] Posts: 1509  Registered: Tuesday, January 10 2006 08:00 
Electric Sheep One
Member # 3431

written Saturday, February 25 2006 13:20
Profile
As a little kid someone defined infinity to me as "the largest number you can think of, plus one". In a way that's still true, because as soon as you learn of an infinity that completely blows your old infinity away, you learn of another one that blows it away. Even the cardinality of the real numbers is low on the totem pole. (Just how low is undecidable  see how fast this gets fun?) Mathematicians do still refer to the 'Absolute Infinity', which is by definition undefinable: the largest number you can't think of. [ Saturday, February 25, 2006 13:29: Message edited by: Student of Trinity ]  We're not doing cool. We're doing pretty. Posts: 3335  Registered: Thursday, September 4 2003 07:00 
...b10010b...
Member # 869

written Saturday, February 25 2006 16:44
Profile
Homepage
quote:No. I'd elaborate, but you can use Wikipedia just as well as I can.  The Empire Always Loses: This Time For Sure! Posts: 9973  Registered: Saturday, March 30 2002 08:00 
Master
Member # 4614

written Sunday, February 26 2006 13:29
Profile
Homepage
Infinity is the slope of the line x=0 and the yintercept of f(x)=1/x.  ben4808 Posts: 3360  Registered: Friday, June 25 2004 07:00 
Electric Sheep One
Member # 3431

written Sunday, February 26 2006 14:53
Profile
That's only a piddly little infinity.  We're not doing cool. We're doing pretty. Posts: 3335  Registered: Thursday, September 4 2003 07:00 
Law Bringer
Member # 335

written Sunday, February 26 2006 18:12
Profile
Homepage
That's not even a defined infinity! —Alorael, who must ponder whether or not the set of all infinite sets is larger than the set of the largest infinite set that is not the set of all infinite sets (if, in fact, the largest infinite set is also the set of all infinite sets). He also must confess that he is less interested in pondering this than saying it out loud and giggling like Thuryl. Posts: 14579  Registered: Saturday, December 1 2001 08:00 
Infiltrator
Member # 4256

written Sunday, February 26 2006 18:44
Profile
Kill me for this, but Chuck Norris counted to infinite and back. Twice. Anyways, infinities are fun, until they turn into head aches. But as an example of larger infinities... Think of R to be the set of all Reals, obviously an infinite set (though a countable one). Then think of R x W to be the direct product of R with W, and unless W only has one element, R x W will be bigger then R. If W is an infinite set, say R again, R x W, will be infinitely bigger then infinity. Then you can repeat for an infinite amount of times, and it keeps getting bigger. And I'm fairly sure that even R ^ (infinity) isn't too high on the 'totem pole'. [ Sunday, February 26, 2006 18:48: Message edited by: AxB ]  "Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'." Posts: 564  Registered: Wednesday, April 14 2004 07:00 
...b10010b...
Member # 869

written Sunday, February 26 2006 19:07
Profile
Homepage
quote:I'm pretty sure there is no set of all infinite sets  there are some classes that can't be defined as sets (at least within ZFC set theory) without introducing paradoxes.  The Empire Always Loses: This Time For Sure! Posts: 9973  Registered: Saturday, March 30 2002 08:00 
Post Navel Trauma ^_^
Member # 67

written Sunday, February 26 2006 23:21
Profile
Homepage
Yeah, the set of all infinite sets would be a member of itself, which isn't the sort of thing ZF likes. R x W will be the same size as R at least for finite W, and probably also for a fair few infinite Ws.  Barcoorah: I even did it to a big dorset ram. desperance.net  Don't follow this link Posts: 1798  Registered: Thursday, October 4 2001 07:00 
? Man, ? Amazing
Member # 5755

written Sunday, February 26 2006 23:35
Profile
We would prefer if you used symbols other than R and W for your games.  quote: Posts: 4114  Registered: Monday, April 25 2005 07:00 
Infiltrator
Member # 4256

written Monday, February 27 2006 04:30
Profile
quote:I was wondering if someone would notice that. Khoth, perhaps you could direct me to a proof of that? Its stands fairly contrary to my understanding of it. R x W, for W = {1, 2} would contain all the elements (1,1) .... (infinity,1) and all the elements (1,2) .... (infinity,2). I believe that would be twice as large as just, 1 .... (infinity)  "Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'." Posts: 564  Registered: Wednesday, April 14 2004 07:00 
Lifecrafter
Member # 6403

written Monday, February 27 2006 04:39
Profile
quote:Limbo is where the good nonchristians go. Purgatory is where the people who were neither good nor bad go. Heaven is where the good christians go. The 10 rings of Hell (I'm not sure if that included Purgatory and/or Limbo, so it may be 8 or 9) is where the evil people go. As for a simple explanation to the "more or less of infinity" thing, using SoT's logic: There is an infinate amount of real numbers (R). There is also an infinate amount of even numbers (E). If R=inf. and E=inf. then R=E. But that conflicts with the statement that R/2=E (as E is only the even numbers), so there is in this case half an amount of infinity that is still infinate. [ Monday, February 27, 2006 04:46: Message edited by: Infernal666hate ]  ??? ?????? ???? ????? Posts: 883  Registered: Wednesday, October 19 2005 07:00 
Raven v. Writing Desk
Member # 261

written Monday, February 27 2006 05:06
Profile
Homepage
Purgatory is not part of Hell. I believe Limbo is supposed to be at the very top of Hell. Also, I may be wrong on this but I think Purgatory was also just for Christians.  Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560  Registered: Wednesday, November 7 2001 08:00 
...b10010b...
Member # 869

written Monday, February 27 2006 05:23
Profile
Homepage
"Size" behaves in funny ways when you're talking about transfinite sets. The closest thing that a transfinite set has to size is its cardinality, and a set's cardinality can't be "twice as big" or "half as big" as another set's in any meaningful sense  it's just bigger, smaller or the same. The set of even numbers has the same cardinality as the set of all natural numbers, but the set of all real numbers has a higher cardinality. [ Monday, February 27, 2006 05:31: Message edited by: Thuryl ]  The Empire Always Loses: This Time For Sure! Posts: 9973  Registered: Saturday, March 30 2002 08:00 
Infiltrator
Member # 4256

written Monday, February 27 2006 06:39
Profile
Ah, ok, I'll ask about it then. Always good to find out where comprehension of something is shaky. I would tend to think that R^2 would be bigger then just R though, as R has a generator (under addition), but R^2 doesn't. But then again, those others don't have generators either, so that probably doesn't mean anything. Edit for some punctuation [ Monday, February 27, 2006 18:38: Message edited by: AxB ]  "Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'." Posts: 564  Registered: Wednesday, April 14 2004 07:00 