How To Count Past Infinity
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- Опубліковано 6 тра 2024
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my twitter: @tweetsauce
my instagram: electricpants
Sources and links to learn more below!
I’m very grateful to mathematician Hugh Woodin, Professor of Philosophy and Mathematics at Harvard, for taking the time on multiple occasions to discuss this topic with me and help me wrap my (finite) head around it.
I’m also grateful to David Eisenbud, the Director of the Mathematical Sciences Research Institute (MSRI) and professor of mathematics at the University of California, Berkeley, for his help and for connecting me with Hugh Woodin.
And of course, big thanks to Brady Haran who created the “mile of pi” seen in this video and connected me with all these mathematicians in the first place. His channel, Numberphile, is superb: / numberphile
BOOKS related to these topics that I used:
“The Outer Limits of Reason” by Noson S. Yanofsky: amzn.com/0262019353
“Infinity and The Mind” by Rudy Rucker: amzn.com/0691121273
“Roads to Infinity” by John C. Stilwell: amzn.com/1568814666
“More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: amzn.com/1551119099
“Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: amzn.com/0486470369
classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: amzn.com/0486488209
Hugh Woodin speaking about infinity at the World Science Festival: • Infinity: The Science ...
Names of large (finite) numbers: en.wikipedia.org/wiki/Names_o...
Geoglyphs:
The biggest number: goo.gl/maps/7GWcpnzo7iG2
Fovant badges: en.wikipedia.org/wiki/Fovant_...
Battalion Park: en.wikipedia.org/wiki/Battali...
A mile of pi [VIDEO]: • Mile of Pi - Numberphile
Wikipedia’s great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Om...
as seen on: en.wikipedia.org/wiki/Ordinal...
this is also a good page about ordinals: math.wikia.com/wiki/Ordinal_Nu...
also: www.cut-the-knot.org/WhatIs/In...
and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order
Axioms:
en.wikipedia.org/wiki/Axiom
/ have_there_been_axioms...
philosophy.stackexchange.com/q...
www.cs.umd.edu/~gasarch/BLOGPA...
www.cs.umd.edu/~gasarch/BLOGPA...
THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES
[PDF]: www.maths.ed.ac.uk/~aar/papers...
en.wikipedia.org/wiki/The_Unr...
Large Cardinal game based on 2048: cantorontheshore.blogspot.it/2...
Other good resources:
quibb.blogspot.com/2012/01/inf...
plato.stanford.edu/entries/set...
cantorsattic.info/Cantor%27s_A...
cantorontheshore.blogspot.co.a...
isomorphism.es/post/1078208142...
lukepalmer.wordpress.com/2007...
MUSIC BY:
/ jakechudnow
www.audionetwork.com - Наука та технологія
listen to what I say at exactly 0:40
K
+Vsauce mind = blown
K
Ok
Ignt
-So can we count to Infinity?
-ℵₒ
@Una Kovacevic idk xd
What?
😂😂😂
§4
Omega + Aleph null = ?
The seemingly random "post credits" scene was incredible.
"Omega + one" indicates a number that is in order after the "last" of the natural numbers. Having that bit play AFTER the "end" of the video was absolutely genius and wonderfully creative.
Least genius vsauce moment:
@@smallw1991 bro had to use Aleph Null of his I.Q. to tell us that part lol
I always watched this video since it has been uploaded and never really noticed this aspect until I read your comment.
The sound ❤ what he is talking about 💀
1:00 How to count according to Michael:
40, 41, 42, 43, a billion, a trillion
It stops at 40 cause it’s the biggest
LMFAOO
But what about 41 42 or 43 44 ?😊
1:67
He’s counting down as he said that 40 was the biggest number
9 year old me: *Infinity plus one.*
Smart alek
@@BMXSymmetry *aleph
Andrew Zhang oof idk how to spell that word thx
@@BMXSymmetry It was a joke, m8
IKR
How to count past infinity:
Dumb people: infinity+1
Smart people: you can’t
Top mathematicians: infinity+1 lmao
lmfao
AHAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@AAAAAAAAAAAAAAAA@AAAAAAAA@AAAAAA@AAAAAAAH
AH HAHA
HA
Whats......infinity - 1
@@jumpyyjasminee5315 Aleph -1
@X3DwAnY - ive always been vonfused mah man
16:03 "we’re cooking now". I didn’t know people said this 7 years ago I thought that only came out last year?? How ahead of vsauce’s time was he?
He's Omega
@@-SPACEBOY- cleverrrrrrrrrrrrrrrrr
expressions related with cooking or eating have been around for quite a while, but it only now got real mainstream thanks to instagram and such. It was funny seeing michael say that tho lole.
He's ω+69 years ahead of all of us
😂😂 gen Z didn’t come up with “let him cook” or “we cooking now”. Your age is showing.
This video is 7 years old yet still feels like it was uploaded yesterday
2017.....
2016* @@SnakeArtsOfficials 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓
2015* 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓 🤓@@alexsummers691
@@alexsummers691 7 years, 11 months and 22 days ago currently☝🤓
🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏🤫🧏
Yeah right?
God: how many years do you want to live?
Queen Elizabeth II:
Hurb
God: how many years do you want to live?
Queen Elizabeth II: Yes
Cristina anduru that was my speech of spelling bruh backwards
Inf
@@warrenlamont8233 v
21:00 and this is why i absolutely love and adore mathematicians they're just like me "oh this is absurd that makes no sense but yknow what let's keep going anyway let's see how far we can go"
So true!
"There was a point in time when we should have stopped, and we have definitely crossed that point, BUT LETS KEEP GOING ANYWAY JUST TO FIND OUT WHAT HAPPENS!"
That diagram is one of my favourite parts of the vid, mostly because of the names that they've chosen. Like, what the hell is "measurable" doing all the way up there?! 😂 And just above it is strong. Just "strong". And then there's huge and almost huge, which I get the sense were discovered in that order somehow.
the fun part is it's absurd but it does make sense
Man, for some reason no matter how hard I try, I cant bring myself to stop watching. I ask myself, "When will i ever use this knowledge?" and my answer is never. But still its so entertaining to watch numbers over numbers of complexity and pretend i comepletely understand and I believe I understand too just because of his amazing teaching. Well Vsauce, you just gained another VERY big fan and subscriber. I got notifications going.
I think it's because he's everything that schools aren't; fun and we actually understand his explanations
The beauty of math is that it invents tools that we don't need now, but MAY need hundreds of years form the now.
The mathematician Euler did some finicky math hundreds of years ago and came to the conclusion that "the sum of all real numbers" was equal to "-1/12". It was a bizarre conclusion that he threw out...
Now whenever a computer calculates infinity, we tell it to replace it with -1/12 and it works. Euler used math to invent a computer algorithm hundreds of years before computers even existed.
Nobody:
Vsauce: How to taste the color 7.
MMMMM TASTY
*_BANANA SUNDAE_*
mr.beast reference
I'm guessing strawberry
It tastes like synesthesia..
Took me a while to realise that's two different sensations and a number.
"Mom, Vsauce glitched my brain again!"
L
Lol
My brain blew up
and my raind turned into poop and pooped
+brualdasil2 this is so easy for a computer science graduate i almost fell asleep in the video.
Important note about the continuum hypothesis (CH): It's not just that it's unsolved, it's actually unsolvable. CH has been shown to be logically independent from the ZFC axioms of set theory - that is, you can show that CH is not a theorem of ZFC and that the negation of CH is also not a theorem of ZFC. This is ultimately a consequence of incompleteness - any set of axioms and system of proofs must contain propositions which are neither provable or disprovable
Unsolvable? That's annoying
what the fuck i didnt understand any of that
@@GalaxPVP Basically: we know that the amount of real numbers is more than the amount of rationals and integers, but we don't know _how_ much more.
@@GalaxPVPThe continuum hypothesis is unsolvable because our logic and axioms are insufficient for defining the value of the power set of aleph-null.
@@andrewpinedo1883 oh ok
“All we have to say is ‘Let there be Omega’, and it will be good.”
Why does this sound like a quote from a fantasy movie lmao
He would definitely be the cool wizard guy that guides the hero
It’s a reference to The Bible, in particular the book of Genesis, about god creating stuff like light.
@@AndresFirte that's a great fantasy book (jk)
Person: what is your IQ?
Me: θ
+G-Town Crew (GTC) i will respond to you so i can copy that swastika later on my computer ( i am now on phone )
He said person.
Ł
smeerkaas fabrikant don't you mean 1 😏
theta?
"There are numbers bigger than 40.. 41.. 42.. 43..
*A B I L L I O N*
*A T R I L L I O N* "
Man that escalated quickly
i mean, in the context of this video, those were puny jumps
not as fast as TREE(3)
Daniel Gonzalez do not
Daniel Gonzalez do not have to be able to get the Playstation the same time as the best way to get the best way to the $ 1356#585376 die , and the City of new York City new Zealand the same time as the first time in my opinion
Tanroop Singh Hey, how's the schizophrenia going?
00:03 Infinity is not a number, but a kind of number.
02:41 Aleph null is a big amount, bigger than any finite amount, but we can count past it using supertask.
05:05 Ordinal numbers are used to label an infinite collection beyond the naturals.
07:30 The order type of sequences and different infinities explained.
09:56 Diagonalization method creates new subsets beyond infinity
12:20 Mathematics is based on axioms and is unreasonably effective in natural sciences
14:53 Axiom of replacement allows construction of new ordinals without end
17:13 The continuum hypothesis is an unsolved mystery.
19:15 Inaccessible cardinals represent a number that cannot be reached from below.
21:25 Infinities may exist beyond the physical realm.
Crafted by Sarthak Naithani *i understand everything albert einstien*
we had dimensions in objects (e.g. 2D, 3D), and the way vsauce described infinities, i think we also found them number dimensions
"0=1"
Yup, I've had enough of math today.
You noticed that too!
It makes sense though!
hey now, if you consider a Field of characteristic 1, then 0 necessarily equals 1. It's just that the only field with characteristic 1 is the trivial field and well... no one actually cares about the trivial field :(
So 0=1 being there is not stating that 0=1 is a true statement. The hierarchy is shown in the order of the strength of the axioms. 0=1 is at the stop because it is so strong that it is inconsistent with our rules of math and therefore anything can be explained using it because at that point everything equals each other. It isn't a true axiom that is actually accepted it's just a cap on the strength of the axioms declaring the existence of larger cardinals. All other axioms lower than it and are weaker than it and, therefore, they remain consistent with math.
Sir Billius So, is it kind of like a math black hole, where there is so much matter that the laws start to shift?
40: exists
41: I'm about to end this man's whole career
42: *growling*
@Silk0 Gaming 1,000,000,000: come again ni**a
1,000,000,000,000: *laughs in the distance*
*Octillion:* aaghh stoop
42 : am i a joke to you
Talk to Chuck Norris. He counted to infinity twice before his first birthday.
Chuck Norris can also pick limes from a lemon tree and make the best orange juice you've ever tasted.
Ima make my own inaccesible ordinal and call it “this is the last inaccesible ordinal stfu and live with it”
Sure. ZFC + "there exists an inaccessible cardinal" is consistent, if and only if ZFC + "there exists exactly one inaccessible cardinal" is consistent. (However, some large cardinal axioms imply that there exists a proper class of inaccessible cardinals, and that's equivalent to the assumption that there isn't a maximum inaccessible cardinal. But if you have a model with a proper class of inaccessible cardinals, you can produce a model of set theory with a maximum inaccessible cardinal, by cutting it at some appropriate place in the von Neumann hierarchy.)
Michael: “how to count past infinity”
6 year old me: *_infinity and one._*
22 year old me: *_infinity and two_* ?
10 year old me: *infinty and infinity*
80 year old me *omega + omega*
Infinity x infinity
0÷0
“I love you infinity +1.”
“I love you 40.”
“Damn”
I love you first letter of the hebrew alphabet 0
Underrated comment
I dont find aluf nol in my keyboard
then love them to infinity and beyond
@@kreckdem_7340 aleph null
I'm in tears (I exaggerated. Actually, better than in tears) and with thrills (shivers? I don't know English) each time I watch this video and the Theta is reached. Really big thanks to you, Michael, for having brought me joy, having brought me sense, after I discovered that atoms are not so tiny, galaxies not so big, the universe not so old (recent history is comparable with the history of life and Earth), that anything material is not surprising but that there are things, actual logical things (don't know how much this counts), that can go even way beyond what satisfies me, my hunger for the greatness and the epicness, and Sense. Sense of life to me is merely complexity. I discovered the magnitude if Graham's number and felt shocked. I discovered these "numbers" in the video, in respect to which Graham's is totally nothing (actually infinitesimal) just in comparison with the first one, the numeral infinite, aleph_0. I will take refuge in the ideal world. Mathematics, with its total rigor, the minimal starting points and its complexity, hasn't disappointed me much, yet.
Something cool to mention is that is that there are TWO infinite sets and 0 is a transfinite gateway keeping positive/negative omega times/power/root of whatever as the same set but anyone that disagrees, I am entitled to my opinion and same for you.
Mom: take a break
Me: Do you even exist?
XD
You got me tho and I'm finally got the second Place of the replied
Trash the PC!
memz lord (vsauce music plays)
memz lord lol
Never discuss infinity with a mathematician, they can go on about it forever.
W
I see what you did there
ayyy
+The TropicDolphin K Q wat
like a neverending argument
Michael, i must thank you, enytime i have a test, i watch your videos and my head suddenly starts to hurt.
i remember, this was the first ever Vsauce video i watched, at my Grandmas house on a laptop. i came back here to say that. ok bye
Fun fact: infinity+1 is bigger than infinity.
Source: 7 year old me arguing with my siblings
lol 😂
Hahaha I remember that “yeah infinity and one is bigger than infinity” *me arguing with my mum while I’m 8
Infinity+infinity b*tch
DOUBLE INFINITY HAS ENTERED THE CHAT
Infinity×Infinity×Infinity
When you look away for 1 second in class:
k Im gonna try this. Im gonna look away for one second next time in my math class, and if michael isnt there youre stinky poo
@@NautsuJJR so what happened?
Did he appear or not
LMAOOOOOOO THIS IS UNDERRATED
@@NautsuJJR i've been waiting for a week for godsake DID HE APPEAR OR NOT?
@@MintylLilGuy It's Michael. He appears everywhere, yet also nowhere. *Or did he?*
I watched this video a while back. Brings back good times.
5:00 the infinate hotel explains how an infinste hotel has infinate rooms and if they are fully booked, you can simply just move everyone down one room to open up a slot
the short infinite hotel video also explains how the infinite hotel could get full. watch that whole video.
ah finally a way to measure your mom's weight
+TheOsva75 fat
W
Look who's talking
+EvilisMe No, really, maybe it was too easy, but i'm laughing anyway
W
Me explaining my parents that u cant pause an online game:
ahahahhahha
Lol so true
True
same
Thats me-
This is the one that started it all for me, the first vsauce video I ever saw
3:34 that drop hits HARD
How to count past infinity:
*40*
41
Rat rat 42
GNM
42.1
43
69.69
The largest number is “error” you can ask the calculator
Specifically a calculation error
That’s true
LOLOLOL FACTS
U can ask yourself sshh yishsyhsbsyusyhsybbbsbsybsybsysnnsuhsnuhs and it will say error
No it 0
I think a set of all naturals is N1 because you could divide N by N to get 1. Then 2^1 is 2. Multiply that by N again and that is N2.
There will be a finite number of atoms in the uni verse timeline there will be a practical biggest number in terms of the universe but to calculate it you would need to know 1. The approximate death date of the universe, and two the universes current size meaning that it is theoretically impossible to answer this question.
"I like your funny words magic man."
I see you too are a man of culture.
@@amyemery6405 e
I am the 69 + 1th like giver.
hahahaha
Nothing bad ever happened to the Kennedys
Arcade Gannon did a service helping you.
short answer: No
long answer: Yes
Vsauce answer: what is answer
Wow 😂
Because yes is longer than no
well yes but acctualy no.
@@hexagon8899 answer is maybe, or not
I love coming back here year after year, just for the exhilarating and visceral vertigo.
I like the symbolism of θ being used to represent the inaccessible cardinal. It looks like a "no" sign, but it also looks like a corrupted 8, in the same way that infinity is a sideways 8. It's also the first letter in "Thanatos", meaning "death."
Therapist: So how much stress are you dealing with.
Me:
Therapist.exe has stopped working
@@vinnyhorapeti2461 I'm just program designed to make ha ha.. A file named "Laugh Man".
I'm confused with the joke
IB Students: Pathetic.
Infinity plus 1 is bigger.
Michael: well, there's 41
Me: ok
Michael: then there's 42
Me: yea
Michael: and then 43
Me: mhm
Michael: a billion
Me: now I'm not sure about this, but I think you skipped a few
Michael: a ᵀʳᶦˡˡᶦᵒⁿ
why do you talk to a screen
why ask
omega looks like a butt or upsidedown 3
Me an intellectual:
Infinity to the power of infinity
ⁿ⁰
23:19 Similarly, ω*2 is not the same as 2*ω. (2*ω is just ω)
10:40 you just wrinkled my brain man
Vsauce videos
Title: Is fire hot
Answers:Yes
Talks about birds for the rest of the video
fat
So very true.
+John Chaser At least they only waste little time and space, while others act entitled and take time to be hurtful.
+Marco Garcia More like
Is fire wet?
No... or is it?
+John Chaser Amazing. Hey! listen! Not everyone has to agree with you! They aren't a specific thing because of that. Imagine saying that in real life. "If you don't agree with me than you are this". That would NEVER happen! I know you didn't say this exact words, but that is the message you are giving. Please just get out of this mindset, and it may effect you in real life. And finally, comment back. I dare you. You will describe how, because I disagree with you, I am a terrible person and brain dead and retareded. But look. Think about it. It is extremely, EXTREMELY stupid! It would be like going into a court room and saying that, even if all the evidence is against a murderer: " You brain dead idiots! I think he is not guilty AND THEREFORE I AM RIGHT!" Again, that would never happen! Take a step back, and look at what you said. Same goes for the guy you were replying to! It's their opinion! DON'T call them fat for it! I swear, the youtube comment section is becoming more and MORE like DEFFOCATION!
“Why didn’t you do your math test?”
*”I don’t believe in numbers.”*
“Numbers are a hoax made by the schools to make me use a pencil! Pencils are know to kill people and they can’t fool me, you sheep”
@@speeder.x9983 true
@@speeder.x9983 ummm okay XD
🙏🏽
infinitist
Axiom = I made it the f up
My source: Axiom of axioms
I think the universe is audacious enough that it does contain the infinities described by math
an audacious universe! a grand and intoxicating universe!
This confused me, then pissed me off, then made me feel so relaxed
+dam7196 i'm pissed again
+dam7196 it's so cool that we have the technology that allows for presentations like this. I'm currently studying the physics of sound (sound itself, the perception of sound, and applications to musical instruments). It would be almost impossible to do learn it with the technology only a few decades ago. this is all so crazy
+dam7196 lol
+dam7196 welcome to Vsauce.
+dam7196 same
This literally, physically, mentally, emotionally, spiritually, chronologically, theoretically, socially, psychologically, metaphorically, and exactly hurt my brain.
Lol same
Well, thank god that it wasn’t hurt literally
@@jacobbishop8067 thanks for the reminder. I forgot that.
Ha
I currently have no brain left and am still getting hurt in all those ways
Here's how you count higher than infinity:
*Infinity one, infinity two..*
Harvard. yo want a scholarship
how are you so smart
Infinity to the power of infinity.
Infinity war...
Hm i guess this is the ENDgame.
*Cringes*
So true
Omega+1 isn't bigger than Omega, it just comes after Omega.
This was when my brain really broke.
-2 comes after -1 (counting from Zero) *but that doesn't make -2 bigger than -1*
Omega Flowey
@@MrAnthonyMarchal Start counting in ascending order from -∞ to -1 *All the best*
Well, if you think about the bananas... it does make sense... I think. These bananas are all equal in form, shape, size and color but they're still different bananas but ordered.
@Gavin DeYager ew ur not supposed to use grammar like that in youtube comment sections
3:27 written out I believe that would be [((10^10^100)!)^((10^10^100)^(10^10^100))]^2 x Graham’s Number
(Sorry if some of the parentheses were redundant)
Graham’s number alone is so big there literally isn’t enough space in the universe to write it out in any normal algebraic capacity. Even googolplex, as gigantic as it is, can be written pretty easily as 10^10^100. Graham’s number might as well just be infinity, but if it’s multiplied by all that, it would get even MORE incomprehensibly big somehow. Even that incomprehensible number Michael named, however, might as well be 0 compared to Aleph Null, which is just the first of a number of infinite infinities which go on forever just like the cardinal numbers did before them.
My head hurts
19:04 The first apperance of a
*legend...*
Mathematicians: “Now... reality can be whatever I want”
math is similar to meth
@@csicee "Bro... I just saw past infinity..."
@@csicee COINCIDENCE !? I THINK NOT !!
@@packediceisthebestminecraf9007 yeah bro it's coooool
My goals are beyond your understandings
waiting for myself to have a son, then I will wait for my son to say “I love you times infinity” and I pull up with the “I love you times Inaccessible Cardinal”
lmfao
Love 100
Or love to the power infinity?
If that was me,8 years old then you had to mess up
i love you times 0=1 :*
Bruh
It has been proven that it is completely impossible in standard set theory (ZFC) to prove the continuum hypothesis even with large cardinal axioms, but it may be provable in other set theories.
If we were to find a proof of the continuum hypothesis (in ZFC), we would have proven that our usual set theory itself gives us contradictions. That is bad news, so let's hope we don't!
Sure, for example continuum hypothesis (and other propositions, like the axiom of choice and generalized continuum hypothesis) can be proven in the following theory: ZF + axiom of constructivity.
I never expected to see an update on this subject. I screamed when I read your comment. Awesome.
@@MikeRosoftJH It's called the Axiom of Constructibility, known as "V=L" (Gödel around 1940). Unfortunately this axiom is widely considered false: V=L fails somewhere around the existence of 0# (21:00). As set theorists consider the mathematical universe to not suddenly stop but to contain arbitrarily large sets (as long as they are not contradictory), V=L must be wrong. In fact only countably many reals are constructible.
The video I always come back to when I think about infinity
teacher: the test isn't that hard
the test:
I pretend to know the answers although I actually don't
Easier to understand than during class
there is 666 likes!!!
Dad:From a scale of 1 to 10, how hard did your brother hit you?
My brother:
They be like that
ℵₒ
This comment made my day
lol
How am i Going chat that no '-'
I am a CS student and your content is absolutely priceless. I took a course about this subject and you helped me to understand infinity better. Complicated and interesting topic. Love your work
"What's your favorite number?"
*proceeds to fully break down the quantum physics of þe universe*
What they teach in class:
12*5
What they ask for exam:
(This Video)
This comment has got 40 likes
@@pranabmohanty7767 wow congrats
12*5 = the amount of likes on your comment
this is so relatable
@@lovelymayapop 60?
Random Guy : How to kill a brain without using any weapons?
Me :
LOL😂😂
But you didn’t put what you would do to kill a brain without a weapon
Yes I know it was a joke so don’t try to woooosh me if u do you will be the one getting wooooshed
@@galactic7458 woosh omega w
Use Math And Science And Even English!
Galactic Banana Capsule R/Woooooooosh
U can't woosh me either cuz I wooooooooshed you not woooosh you and in ur comment u said woooosh and not woooooooosh
4:19 zoom in those numbers are actually in order idk why but it’s cool
This might be the coolest video on UA-cam
Nobody
Vsauce: How to disable fall damage in real life
Lmao idot just do /gamemode 1 hahahahaha
if you jump from a 86 floor apartment you can fly thanks to the spirit of shaggy
Caboose /gamerulefalldamage false
You need cheats enabled just to let u know
Just use creative mode smh.
I know this isn't related but how did you get the infinity symbol.
"there's always a bigger fish"
Ah yes, good old Qui Gon
AND THE BIGGEST FISH
*IS ME*
Good quote.
"Little fish, big fish, swimming in the water..."
111511116614inches 1415feet 18151541411415815195526288258627285251614151551851711415144 miles
Vsauce you were in the Australian academy of science for this video!!!
dude the end is always the best part
My brain broke when he said "Hey Vsauce"
+Chiseled Knucklez This time he didn't start the video by "when do you die?", though.
hah
My mind was blown before I even clicked the video
same
I had to cry in a corner 3 minutes in.
"How much do you love your homies?"
Me:
Olive no
Bruh 🗿 bruh 🗿 bruh 🗿 bruh 🗿 thasss good one
No homo
That's the most gay comment I've ever seen
vishnu pypy lol true
So actually not thing bigger than infinity, just arranged differently. And to create a larger infinity we must "multiply" the two infinity together (create an infinite sequence arrangements with infinite elements in a spreadsheet format and reason that there is always an unlisted sequence arrangements). I personality don’t think we can even do that cause how can we list end less thing and arrange them end less time? Or just imagine? In fact, infinity is already INFINITE. Creating something larger than infinity is just a recognized concept that speaks to human imagination (although I think people still haven't imagined what exactly infinity is) but they still want to get over it.
Wait.... what about..
Replace the "0" in "aplph null" with another "alaph null" and continue the process for a 'alaph null' times
yep, that exists. Its the first number to satisfy x = omega_x
"infinity is not a number"
8 year old me : impossible...
Xander Shrive hey. not everyone is as smart as you, and he was making a joke. just laugh
More like me yesterday XDD
T~T
@Xander Shrive me an angry bird player with mod inf: yes
Yep, I same way :p
Micheal: What is the biggest number?
1 billion! INFINITY! A googol!
Micheal: No its just 40
Oh
BooceBooce Michael*
41,42,42,44,45,46,47,48,49,50...
MARIOPLEX!
41: am I a joke to you?
OR IS IT?????
Love this so much! It's a blurring of math & myth.
He just makes me question my existence and then says "and as always... thanks for watching"
In high school I was telling my friend about omega and I got a detention for drawing "balls" on my paper ....
Bruh
bruh
+luke scott bruh
+Kelly O u ruined it
Yuya Fujisawa Perhaps
**opens video**
“Ok ok numbers I understand this.”
**a few minutes in**
“I am confusion...”
DeathStar14 explain vsauce explain, what do you mean past infinity
DeathStar14 is confused!
DeathStar14 used Death laser!
The laser turned 180° and hit DeathStar14!
DeathStar14 exploded!
Wat
same
So I am confusion.
Why is THIS ONE **points to Kansas** called can-sas but THIS ONE **points to Arkansas** called ar-can-saw? AMERICA EXPLAIN
Yeah in the first 3 minutes I was totally confused. And after that I thought holy f##cking sh#t I am so f##cking dumb compared to this guy.
Ordinals *do* appear in a natural way, since they are basically the hierarchy of deepness.
For example, you can think about a table.
Well, now you are thinking about thinking about a table.
Are you now thinking about thinking about a table? No. You are thinking about how this could go on.
This thought has a depth of ω.
But it is really fundamental to mathematics when you consider that mathematical is build from itself, you can order the assumptions.
Getting infinite ordinals is equivalent with using induction in a proof.
This guy gets it. This defines all recursive ordinals directly and then all ordinals thereafter, if you just accepts a few hypercomputational operations as axioms.
Bro really said to infinity and BEYOND
My niece: "I've figured out that the biggest number is 983!"
Me: "Haha. What about 984?"
My niece: "Argh! I was so close!"
Lol thats cute
707 69 upsidedown is 69 lol
@@kasimhanif3478 Mr funny smart
DannaBannana you just made my day
XD
I’m so simple-minded that I can come back and watch old Vsauce videos and still be absolutely mind boggled as if I’m learning it for the first time
@eg same x2
Same here 🤗
Same
Makes me happy being a dummy because I know I'll never run out of vsauce content
Damn this video is truly crazy
WARNING, Long comment ahead!
Going back to what he had said about an unreachable number after the unreachable numbers, if there is something above everything, then the only way to reach it would be to create true infinity, a number or creation that NEVER stops and has no unreachables above it.
But then again, perpetual things only exist in theories and ideas, not in the physical realm, and yet they do exist.
Schroedinger's cat is an example of this. It is something that until viewed is a paradox, it both exists and doesn't, if we ever view both sides we will have reached a new unreachable.
Just like how there is only 1 universe, at the same instant, there are infinite universes, if there is something in one universe then there could be that same object EVERYWHERE at the same time, if it's everywhere at the same time then it could be every time in the same universe.
Math, science, and even human nature all say different things,
Like how human nature is to search, science is to experiment, and math is to solve. All have their uses, but they can never agree.
A paradox is something that cannot exist yet it does, there are many, Many, MANY unexplained phenomena from humankind's recorded history that are shelved and collecting dust, which is what they both should and should NOT be doing.
Every time a new unexplained thing happens, we try to figure it out and then stop. What we should be doing is trying to create the EXACT same thing and keep the knowledge we'd learned.
Think about all of the technological advancements of human history, all of them were from something outside of human control or knowledge giving or showing us something, I'm not being religious about this, if things can exist in each dimension (1D, 2D, 3D) then why can't there be another dimension we can't see?
Perspective, that is why. If a 1 can't see a 2, and a 2 a 3, then why could a 3 see a 4, or a 4 a 5? It's all perspective, when you learn to slow down and feel (not see, think, or even know), you can notice a lot more about the world around you than ever before.
Few people have done it by true calm. Most go through rigorous training and mental struggle to learn more about themselves and the world, and that is the problem.
Let yourself go and fall into the rooms inside your head because the first step to seeing more is to see less, close your mind's eye to all things and just start to focus on what you can visualize around you, don't think about what you had seen before hand, just visualize what your mind feels.
Once you have learned to visualize what can't be seen, you will notice more about the world than others before you.
If you've read this far then congrats, you've learned more than most other people would. If you just scrolled to the end and didn't read it all, then you have proven to be an impatient person who fears to learn.
Thank you for reading this, and I hope you've learned to visualize more of the hidden world around you before you see the opinions put before us😌
Dude, get some definitions for the things you're talking about it's impossible to understand what you're saying, like what exactly is a "perpetual thing" and what about them makes them only "exist in theories and ideas, not in the physical realm", and for that matter what do you mean by "physical realm" and "theories and ideas". Not to be mean, but it's just vibes and talk, no real work has been done here with this text.
If people who are dealing with insurmountably large sets are getting 0=1, I think its important to note that it doesnt suggest its true. It may be that its a sign they're wrong, or something they assumed, concluded after large amounts of work to be incorrect.
Take for example the expression 3x = 2x. You can try to reduce it by removing the x from both sides, or dividing one side by the constant then the other by x, but either or you will be left with 3 = 2, 2/3 = 1, or 3/2 = 1. This doesnt mean that 3 is equal to 2... It simply means the expression I initially wrote is in its entirety, incorrect. 3 does not equal 2. Excluding 0 as a solution, 3x will never equal 2x for any real number x.
For your purposes, I think something like x = x + 1 would've been a better example to use. I guess it's true that, excluding x = 0, the equation 3x = 2x has no solution for x. But if you chose to make that exclusion, then you should've mentioned it from the get-go.
Dividing both sides by x isn't really how you're supposed to solve stuff like this; after all, there's the possibility of x being 0, in which case dividing by x gives you nonsense. Here, the correct method is to subtract 2x from both sides, yielding x = 0. It's easy to see how dividing by x went wrong here, but more insidious is a case like x^2 = x; here, dividing both sides by x gives x = 1, which is indeed one solution, but the solution x = 0 has vanished.
Why am I so obsessed with watching videos that make my brain dissolve itself
because of the natural occurrence of any animal having curiosity in something that interests or sparks their mind, creating a mental 'explosion'.
Because you are a human
I like the pictures
Notis Senju agreed
No, no, no, no, no, no, no, no.... for infinity. When I have reached the an infinite number of "No" then I will say yes to this logic.
"that means that an infinite amount of people finished the race... And then, YOU did."
:'(
Junn Cali lol
#relatable
But they are all winners if it's a school race :-P
Land Rover Addict 😂 this is so true
me: hey mom ok ready
Mom: ok son
me: REEEEEEEEEEEEEEEE
Every time I scare myself with the grin I am having when rewatching and realising unlimited power of axioms and infinities
these vids are such great background vids even though i dont understand any of it
It makes sense that 40 is the biggest number. It's extra large (XL is 40 in Roman Numerals).
Oh man!!!!
Then what's XXL or XXXL or XXXXL or M or.........
omega + L :P
That's actually cool.
@@ishantyadav5532 There is no XXL Roman number. X means 10 and L means 50. Placing a smaller number before a bigger number means substraction, so therefore XL means 50-10=40. XXL would mean 30 by that logic, but that slot is taken by XXX, which means 10+10+10. Note that you can't put more than 3 of the same number next to each other and make things like XXXX, that's is where XL comes in place.
@@owl1095 roman #'s are weird like how do you write 100k without writing M 100 times
Good one!
rip brain
right
bottom
ambidextrous
Every Vsauce video is RIP
Lol
What an super-interesting video, thanks a lot!! My comment to the last thing said in this video: Humankind had created something outside this physical universe some 2.5 thousand years ago: Euklid discovered the square root of 2. Not anywhere in our physical (!) universe is there anything, that has the physical amount of the square root of two. (and many more, of course)