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(Quanta Magazine)   We may just wrap our heads around infinity after all   (quantamagazine.org) divider line
    More: Cool, Set theory, Zermelo-Fraenkel set theory, Continuum hypothesis, Axiom of choice, Georg Cantor, Real number, Mathematics, rival axioms  
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1271 clicks; posted to STEM » on 22 Jul 2021 at 1:17 AM (13 days ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook



33 Comments     (+0 »)
View Voting Results: Smartest and Funniest
 
2021-07-21 7:08:59 PM  
It's just the luxe brand of Nissan. Kinda speaks for itself, Subby.
 
2021-07-21 9:14:47 PM  

dammit just give me a login: It's just the luxe brand of Nissan. Kinda speaks for itself, Subby.


There's a lot of different sizes of Infiniti, though.
 
2021-07-21 11:44:33 PM  
Infiniti Toilet: Cup Holder - Saturday Night Live
Youtube 6IR9jgR7oDM
 
2021-07-21 11:48:16 PM  
Infinity....and beyond?
 
2021-07-22 1:41:16 AM  
You can always add 1 to it ..
 
2021-07-22 2:19:13 AM  

mikalmd: You can always add 1 to it ..


That's apparently not always true.

Math is a human creation, but each system comes out of a basic ruleset or assumptions or something. I lack the jargon, but look up Göedel(sic) to get what I'm talking about.

Everything else is derived from those basic rules(sic). it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc
 
2021-07-22 2:32:46 AM  

leeksfromchichis: it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc


YR-M0M's so big, you can't possibly add plus one?
 
2021-07-22 2:41:51 AM  
Just yesterday I mention the uncountability of the set of real numbers in a different thread, and today we get this. Maybe I should mention more math stuff.
 
2021-07-22 2:44:48 AM  
Someone reconciled determinancy and choice, which means I now doubt determinacy.

Actually, in seriousness, by my amateur understanding of this it doesn't sound that impressive.  It sounds like they proved that Axiom A (Martin) and Axion B (choice) logically implies the truth of Axiom C (star) under Axiom D (determinacy) and vice versa.  I.e., you take choice as an axiom, the theorem says that if you remove choice from your universe, add determinacy, and them take star as as an axiom tn that universe, it logically implies Martin in the original universe.  Which only moves the goalposts, really.
 
2021-07-22 2:46:12 AM  

emtwo: leeksfromchichis: it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc

YR-M0M's so big, you can't possibly add plus one?


Exactly.
 
2021-07-22 2:49:52 AM  
Fark user imageView Full Size
 
2021-07-22 3:04:45 AM  

aerojockey: Someone reconciled determinancy and choice, which means I now doubt determinacy.

Actually, in seriousness, by my amateur understanding of this it doesn't sound that impressive.  It sounds like they proved that Axiom A (Martin) and Axion B (choice) logically implies the truth of Axiom C (star) under Axiom D (determinacy) and vice versa.  I.e., you take choice as an axiom, the theorem says that if you remove choice from your universe, add determinacy, and them take star as as an axiom tn that universe, it logically implies Martin in the original universe.  Which only moves the goalposts, really.


If you choose not to decide, you still have made a choice.
 
2021-07-22 3:07:53 AM  
I work with, among many other eggheads of various disciplines, abstract theoretical mathematicians.

It's my firm conclusion, based on direct experience, that people who understand this shiat aren't right in the head.

They're fine people, to an individual.  There's not one I wouldn't trust with a secret if I asked them for confidence.

But most of them I wouldn't trust to make coffee.

And some of them are upper-level managers.  The fact that I think it's a good thing that an accountant is the general manager of that organization tells you all you need to know.
 
2021-07-22 3:32:55 AM  
You can't count all the numbers because once you reach the end you just add 1 and now you have to start all over again.
 
2021-07-22 3:47:05 AM  
Mr. Show - 24 is the Highest Number
Youtube RkP_OGDCLY0
 
2021-07-22 4:34:49 AM  
Graham's Number - Numberphile
Youtube XTeJ64KD5cg
 
2021-07-22 7:04:52 AM  

Marcus Aurelius: dammit just give me a login: It's just the luxe brand of Nissan. Kinda speaks for itself, Subby.

There's a lot of different sizes of Infiniti, though.


If Infiniti made a semi truck and car carrier trailer, and loaded them up with Infinitis, would it just be Infiniti?
 
2021-07-22 7:33:50 AM  

aerojockey: Actually, in seriousness, by my amateur understanding of this it doesn't sound that impressive


This sentence is entirely self-consistent, which would make Godel unhappy.

Seriously though, having written that sentence, the rational* next step is to say to yourself "Apparently, my amateur understanding is inadequate and/or the article doesn't convey the full power of this". The world would be an infinitely better place if more people did that.


*Insert your own "real next step" or "irrational next step" here. I don't have time as I have an infinity to count.
 
2021-07-22 8:44:07 AM  

leeksfromchichis: mikalmd: You can always add 1 to it ..

That's apparently not always true.

Math is a human creation, but each system comes out of a basic ruleset or assumptions or something. I lack the jargon, but look up Göedel(sic) to get what I'm talking about.

Everything else is derived from those basic rules(sic). it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc


Graham's number doesn't come close to infinity, as shown in the video posted in the thread.

The thing about infinity is that it's not a number, it's a count.
Infinity is bigger than you think - Numberphile
Youtube elvOZm0d4H0
 
2021-07-22 9:12:51 AM  

leeksfromchichis: mikalmd: You can always add 1 to it ..

That's apparently not always true.

Math is a human creation, but each system comes out of a basic ruleset or assumptions or something. I lack the jargon, but look up Göedel(sic) to get what I'm talking about.

Everything else is derived from those basic rules(sic). it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc


Graham's number was, at the time of its publication, just the largest number ever used in a published mathematical proof.  You can always add more to a number.  It may break some proof, but that doesn't mean the number doesn't exist.
 
2021-07-22 9:37:45 AM  
All this infinity talk goes to prove that:

One is the loneliest number
One is the loneliest number
One is the loneliest number that you'll ever do
One is the loneliest number
Much, much worse than two
 
2021-07-22 10:00:35 AM  

Explodo: leeksfromchichis: mikalmd: You can always add 1 to it ..

That's apparently not always true.

Math is a human creation, but each system comes out of a basic ruleset or assumptions or something. I lack the jargon, but look up Göedel(sic) to get what I'm talking about.

Everything else is derived from those basic rules(sic). it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc

Graham's number was, at the time of its publication, just the largest number ever used in a published mathematical proof.  You can always add more to a number.  It may break some proof, but that doesn't mean the number doesn't exist.


Fark user imageView Full Size
 
2021-07-22 10:08:59 AM  
chrisrbfay.files.wordpress.comView Full Size
 
2021-07-22 10:14:09 AM  
pre determinism just took one in the nads, that's what it means.
 
2021-07-22 11:32:11 AM  
Fark user imageView Full Size
 
2021-07-22 12:26:41 PM  
All infinities are infinite, but some infinities are more infinite than others.

2^0 > 0     Or so I am told.

I thought it had to do with all the sets that can made from the numbers in a number, like for 3 there's (1) (2) (3) (1,2) (1,3) (2,3) .

Farked if I know, I've never even took calculus. I just remember bits of what my dad, and a math professor told me when I was 12.
 
2021-07-22 1:08:21 PM  

aerojockey: Someone reconciled determinancy and choice, which means I now doubt determinacy.

Actually, in seriousness, by my amateur understanding of this it doesn't sound that impressive.  It sounds like they proved that Axiom A (Martin) and Axion B (choice) logically implies the truth of Axiom C (star) under Axiom D (determinacy) and vice versa.  I.e., you take choice as an axiom, the theorem says that if you remove choice from your universe, add determinacy, and them take star as as an axiom tn that universe, it logically implies Martin in the original universe.  Which only moves the goalposts, really.


Such proof is self recursive, which renders it inconclusive until P vs NP is solved.
 
2021-07-22 1:13:59 PM  

patr55: pre determinism just took one in the nads, that's what it means.


Post determinism, prune determinism, and alpaca determinism are fine
 
2021-07-22 1:40:58 PM  
Great article, Subby. Nice find.
 
2021-07-22 1:52:31 PM  
I hate math, so I have nothing to really back this claim up, but...why would numbers ever end? They never existed in the first place.

Have another bottle of schnapps, math nerds.
 
2021-07-22 2:03:59 PM  
Still the only diploma I've ever needed

i.imgur.comView Full Size
 
2021-07-22 4:44:43 PM  

Explodo: leeksfromchichis: mikalmd: You can always add 1 to it ..

That's apparently not always true.

Math is a human creation, but each system comes out of a basic ruleset or assumptions or something. I lack the jargon, but look up Göedel(sic) to get what I'm talking about.

Everything else is derived from those basic rules(sic). it's possible to make numbers so big you can't in fact add one anymore without breaking the rules. And that's apparently important enough they name them.  Graham's number, YR-M0M,  TREE3 etc

Graham's number was, at the time of its publication, just the largest number ever used in a published mathematical proof.  You can always add more to a number.  It may break some proof, but that doesn't mean the number doesn't exist.


Did you stop reading at Graham number?

It was a long wind up to a your mom joke.  Emtwo got it
 
2021-07-23 3:34:14 AM  

tuxq: why would numbers ever end? They never existed in the first place.


take that back yo monster
 
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