What is the Largest Number?
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- čas přidán 7. 07. 2024
- What is the biggest, largest, meanest and most terrifying number ever to be conceived?
www.livescience.com/18272-infi... (Does the shape of our universe really prove that a physical infinity exists?)
www.livescience.com/37142-blac... (Is a black hole's singularity really infinitely dense?)
www.princeton.edu/~achaney/tmv... (Hilbert's Paradox of the Grand Hotel)
www.livescience.com/31981-goog... (Googol and Googolplex)
education.jlab.org/qa/mathatom... (How many atoms in the human body)
education.jlab.org/qa/mathatom... (How many atoms in earth)
www.universetoday.com/36302/at... many atoms in the universe)
phys.org/news174921612.html (Number of different possible Parallel Universes)
mathworld.wolfram.com/SkewesNu... (Skews Numbers)
googology.wikia.com/ (Wiki dedicated to large numbers)
planetmath.org/knuthsuparrowno... up-arrow notation)
mathworld.wolfram.com/GrahamsN... (Grahams Number)
planetmath.org/conwayschaineda... (Chained Arrow Notation)
www.math.osu.edu/~friedman.8/p... (TREE(3))
djm.cc/bignum-results.txt (Loader's Number)
web.mit.edu/arayo/www/bignums.... (Article written by Agustin Rayo)
mathfactor.uark.edu/2007/04/ch... (Interview with Rayo) - Věda a technologie
I like the fact that Graham's number is the upper limit of a range, which means the value they could be looking for might be 24.
There leaves a lot of room for dimension where all the lines of said dimension can't exist without crossing each other.
You are my son
the lower bound is 13
but the most interesting is that it can’t be any bigger than G64
Just imagine beings being able to transit through those dimensions!
Pre-schoolers don't know that mixing up "three" and "tree" can become a number so huge, it's unthinkable.
@@coolestcars1983 "googol" isn't a useful number, nor does it follow normal naming conventions for numbers. And "rayo" is the highschool yard version of "Yeah...well... infinity plus 1!"
Beat me to it.
@@coolestcars1983 and SSCG(3)
kid: *accidentally says TREE(3) instead of 33*
me: HAHA REALLY BIG NUMBERS GOIN ON HERE
HEY! I KNOW WHAT TREE(3) IS AND IM IN GRADE 3
"The solution is between 11 and Grahams number" .. can I just write this as an answer to every question at a math test? It will probably be a correct solution most of the time XD
"2+2= "
Mr. Duck o crap
Sure, if you can prove it, and there's no reasonable way to whittle down the answer to something more accurate!
One of the reasons why Graham's Number is important is that it provided an upper bound to a particular problem that, at the time, was boundless -- and since then, the upper bound to the problem has been whittled down considerably.
“If x=x, then how many possible solutions are there?”
Sorry but you’d get that question wrong
@@bruhmomenthdr7575 lol
To help understand how large TREE(3) is,
TREE(3) - Graham’s Number ≈ TREE(3)
Compared to TREE(3), Graham’s Number is basically 0
Ok
TREE(10^100)
@@jameshunt8116 Tree(G64)
@@ldrgoogolplex4683 FOOT^10(10^100)
If you substract G64 from TREE(3) a G64 times the answer is still basically TREE(3)
Hilbert's hotel sounds like a shit place to stay... Moving to the next room every time someone wants to check in...
Yeah, but dont forget, how late you ever come there is always a room to rent.
It's an imaginary hotel. Not actually exist
Roy Wardenaar ask them to build an extra room near the main hotel *Lenny face*
Pc Stuff room not floor
I know room service has got to be terrible
The temperature, in degrees Kelvin, of my mixtape. That's the largest number.
Guys, stop talking in inverses, Its getting a bit cold for my taste here.
+Sod Alfredsod Stay frosty guys, we got a cold-blooded person right here.
+Sod Alfredsod yes
It's On Fire
Its just Kelvin, not degrees Kelvin.
people: something-million
Me, a person who watched all parts of very large numbers: indescribable cardinal
Me: Haha I pity the fool he didn’t watch the end.
Also Me: *Absolute Infinity*
You watched all the videos? I don't have the time for it 😂😂
Boogilgandigan and Goobawamba are two odd names for oddly large numbers.
The rules stated no infinities.
5 years ago I added this video to the "watch later" list. Sadly, I had too little experience with English and mathematics to understand anything you say. Today, I came back. I am finally worthy
ok g
@@ilikechippies2551 truck
@@Orincaby k
"It has to have some use..." including the use of being the largest number??
@@katakana1 Except Googologists view it as essentially unable to be accurately defined, so for now Rayo wears the crown.
@@adamcole4623 Yep!
😂
Vsauce: "40 is the biggest number...
On earth in terms of surface area"
40²? 40³? 40⁴?
40googolplexianianian
XD I've seen that, excellent reference
ew
@@mishka2892 yeah me too that was funny
"numbers have an end"
-Muhamad ababou
Shaawaiz Haider
XDDDDD WTF MAN UR GOOD WELL NOT BETTER THEN UE MUM OHHHH
Sorry man that was my drunk britha
Him did you say there were infinite numbers
PSYCH!! That's the WRONG numbah!!
3^^3=7,625,597,484,987twoarrows
OOOOHHHHHHHHHHHHHHH
anafranil gunk
🤣🤣🤣🤣
Kids trying to be relatable:
I find the fact that a 7x7x7 Rubiks Cube has more permutations than there are atoms in the observable universe astonishing. Imagine how many permutations all those cubes would have if you took all atoms in the observable universe and used them to build Rubiks Cubes.
Now thems some big numbas yes yes, I think that is what Graham's number pertains to actually. Very big, more numbers than a mind is literally capable of containing. BIG
Chuck Norris could still solve it.
I appreciate how you spelt Rubik's correctly
vsauce 4?
here is how to get to tree(3): imagine you have a single colour (this is how to get to tree(1)), say red, the first 'tree' you make has to have at most 1 dot (in red)(also note that every tree must contain at least one dot). the second tree you make has to have *at most* 2 dots in it (in this case also in red).the catch is no previous trees can be contained in later trees, so in other words you can't have all the points in a previous tree connected to the same *closest COMMON* point, meaning tree(1) is just 1. tree(2) is 3 but tree(3) is absolutely humongous.
Felix Roux so big that we have no meaningful way to describe even the number of digits it has in base 10. It’s not exactly known, but even it’s lower bound is an incomprehensible huge number which can only be defined through a recursive function.
@@huckthatdish in base TREE(3) its 10
why did i get so many likes? use a time machine to find out
thanks for this
Wow...
Then add 1 too googlequinplex and it’s a larger number..
How long did this take u
And the Mario plex is no an official number i can’t write it because it’s so big CZcams can’t candle it so here’s a tiny bit of it
100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0 really it’s a really tiny bit I cut it 3 times
My brain broke when you mentioned the 7x7x7 Rubik's cube.
Kalevi Rotmg There are even more possibilities for a 16*16*16 Rubik's cube.
Duh.
Kthulhu himself Of course! But the fact that there are more combinations in the 7x7x7 cube than there are atoms in the universe was mind-blowing.
Also, the 5x5x5 cube is so far the "hardest" cube I can solve. :/
Kalevi Rotmg It isn't really that mind blowing...
Yet still.
Kthulhu himself It is for me. :P
Kalevi Rotmg and then there are Rubik's tesseracts.
the total number of planck time intervals experienced by every plank legnth (cubic) in the observable universe is around 8.3x10^126.. at least we can beat googol in our own universe ">_>
We can do that with a much greater margin: All possible combinations of all atoms in the observable Universe is a number beginning with a 1 followed by approximately 10^80 zeros.
If the multiverse tend to exist than it's said that the average distance between universes based on the observed rate of expansion in ours would be between a Googol and Googolplex light years apart.
10 (^10)x100
Aids number
10 (^10)x10 (^10)x100
Aries number
Actually, WE CAN BEAT A GOOGOLPLEX!! :D, the number of possible combinations of each particle in the Universe is 10^10^10^13.
I’m looking forward to part 2 of this series, then 3, and 4, and so on
for infinity.
Infinity is allowed there.
In ten years they’ll be saying, “remember when we thought Rayo’s number was big.”
Man what a flashback to see your channel in my feed. I used to watch your videos religiously.
Everyone posting numbers just mashing their keyboard clearly dont even grasp what arrow notation is
Not even starting about the G's part
Every number you can mash on your keyboard is incredibly small compared to just 3 arrow arrow arrow 3
The largest number is 42.
All other numbers are either multiples of or divisions of all or part of it.
Go ahead, try it.
:O
By that logic, the largest number is 1
All other numbers are either multiples of or divisions of all or part of it.
Go ahead, try it.
Read "Hitchiker's Guide To The Galaxy".
TacomaPaul I know, I've read it. 42 is the answer to the ultimate question of life, the universe and everything.
TheScoutPro And there ya go.
me:the pasword is on the back of the router
the back of the router:
Ironically, it's numberphile that ended up explaining TREE(3) and Rayo's number to me....
And I got a pretty good understanding of different infinities between them and vsauce.
sharkee = middle eastern vsauce
... yes... Just yes...
Yup Your Right
HE'S EVEN BALD AND GLASSES
Why end at G64? Why not G65 or even G9999999999999999999999999999999Googolplex to the G999999999999999999999999th power? Then multiply that number by a googolplexian? Then you can STILL add one to it. There is no largest number. You can always add one.
But thats not allowed...
Lets do this:
(G64^10^10^10^100^TREE(3)^(10^10^10^100^(G64)))!(G64)
Its Grahams Number to the power of a Googolplexian to the Power of TREE(3) to the power of another Googolplexian To the power of Grahams Number again. And of this you take G64 the Factorial of this.
This would be so large, you wont be able to write the number how many digits the number of the amount of digits of the amount of digits this piece of shit would have
Retroundmike You missed some paranthases dude..but I get the idea.. :D
Because G64 was a specific number used in a mathematical proof.
Obviously, there is no largest number, but he set down some rules at the beginning of the video. Basically, what is the largest number that's ever been used for something specific. And G64 was used in a proof.
***** Well but you can say that there are less particles in all possible universes and all imaginary universes.
and by "G64 the Factorial" i mean G64 !'s behind that
Yeah dude biggest number ever. (Adds 1 to your number)
4:34 imagine if he said that without the text showing up
SCG(13) is bigger than TREE(3) + Tat’s Number is G128 if you wanted to know, Rayo’s Number is also the biggest known number I know.
*Rayo’s Number + Rayo’s Number* = ?????????????????????????????
SpaceOrca equals rayos number squared
SpaceOrca Rayo's numberx2
+ 1...
Rayos#(rayos# of up arrows)rayos#
infinite to the power of infinite
lol...Rayo's number is literally just "the smallest number bigger than whatever you say" doesn't sound any better than saying "your number +1" to me.
"Your number + 1" would be relative to another value, so would be "the biggest number that is not infinity" - such relative numbers could never be "the biggest". Rayo's number however is by its definition an absolute (even if theoretical) value, thus legit.
***** It's still relative because it essentially set down rules for what the biggest numbers could be, and then just said "whatever is bigger than that."
Itachi Uchiha Grahams number is the fcking larg number
nadjim73 Well, Graham's is G64, so keep going, G65, G170, G282475249....
Cooper Gates Yeah but it's at least useful. Otherwise you could, essentially, make G(G64) and just put Graham's Number to its own level and make a number so absurd that nothing can touch it.
12:25 - TREE(3) is so large is impossible to comprehend it in simple terms -
Next video: *The Enormous TREE(3) - Numberphile*
Me after watching the video - Oh, that's clear -
That video doesnt explain anything about TREE(3) because to explain it requires understanding some quite complicated maths. There is no simple way to explain it why it grows so rapidly after TREE(2). In comparison Rayo's Number is much easier to explain. Just explain symbols used in first order set theory and how they all work, then imagine an expression a googol symbols long and that expression expresses Rayo's Number. Just like 10! (10 factorial) expresses 3 628 800
It's so large the growth rate of such a theorem can't even be explained using the FGH.
Yes it can. The growth rate of TREE(n) falls between the SVO and LVO in fgh. I can confirm this because i looked at googology wiki which explains the TREE sequence
These ordinals are beyond gamma zero in fgh
These ordinals are beyond gamma zero in fgh
Every year I come back to this video just to relearn about numbers... I can’t help it... this video is so entertaining
The other guy could have won by saying "Rayo's number +1"
No "BlaBla Number +1"
it should definitely count!!!!!!!!!!!!!!!!!!!!! :()
;) ;););):):):)
Logo so Rayo's number times 2
MozartJunior22 i might be late for this, but if Rayo said infinity, it would always be a tie
If a regular Rubix cube can create such a big number, imagine a Rubix cube as big as the observable universe and every face is as small as a plank length...
Joelimations n’ stuff the plank radius of the universe is 7.04x10^61 and the volume is 4.65x10^185. assume you could get a cube to fit that's a Google length width and height (10^100 close enough) each plank length being a square on the cube. With a rubiks cube (3)x(3)= 43,252,003,274,489,856,000 and 7x7= 1.95x10^160 even if you put a (Google)x(Google) and the answer was raised to the same correct magnitude of a rubiks cube that size you still wouldn't scratch grams number. If every square plank had the same size cube as the one that would fit in the entire universe and you took all the possibilities of out comes from all the cube you would still not even scratch g2. NOT EVEN CLOSE
Congratulations, you bugged me
U spelled rubiks wrong
Well if you see, 43^00-31^01 (Made it up.) IT IS 43^00. which is 43,000,000,000,000,000. (43 Quintillion)
dude dude wow you are impressive
Tbh, TREE(3) is easier to explain where it comes from than Graham’s Number. It’s just playing a game, sure there’s no proper notation to show how massive it is, but the game of trees is easy enough to explain.
Yeah, and G(64) does not have any more use to mathematicians as it is no longer the upper bound on the problem it was used for. With TREE(3), on the other hand, we can only expected the known lower bound to get bigger over time.
Great video, I like your passion for the large numbers.
You ever take a dump and it stunk?
The largest named number currently in existence (according to Googology wiki) is called Little Biggadon. I haven't looked up what it is exactly to preserve some of my sanity, but I know that it did beat out Rayo's number as well as BIG FOOT, which is an extension of the same principle used to get Rayo's number. So it's pretty huge. I don' think its useful for measuring anything though.
Harrison Shone ur wrong bigg beggedon aka sasquatch is way bigger than little beggedon also utter oblivion is 2nd biggest named number and first. Is sams number i researched it on googology.wiki fandom lol
Lucas Lucas Sam’s number doesn’t count according to the site because of how unsourced and poorly described the “number” is
Sam's number is a joke, a pretty obvious joke
@@platypuschallenger it’s not. It has no citation and it was easy to make. The number is completely indescribable, which easily beats any other number at the moment. It’s simply a fact lol
@@NearChannel2576 ...do you even know what the definition of sams number is??
"I suggest you go sit on a toilet now cause things are about to get insane"
*gets out of bed to go sit on toilet*
Rayo's number can be expressed by this sentence and since the sentence can probably be described in set theory in less than a googol symbols, it is self-referential. Therefore it isn't any different than saying " the smallest finite number bigger than any previously used number (aka for integers: x+1)
Rayo's function is not self referential
How do you say "On Crack" so calmly. I laughed at that moment so much.
when did he say that
Infinity is an easier number to understand. weird.
Infinity isn't a number, but you might be right lol.
The concept of infinity drove Georg Cantor insane. It's not so easy to understand either.
Rayo's number + 1. Ha
Garrett Guitarman I guess you threw a rule or two out the window.
Cooper Gates Rayo's number did too.
★ Cuddlepuff ★ Yeah, it and Loader's were just in contests (with terms and conditions). G64 wins according to the original 4 rules.
Cooper Gates Actually I think Tree [3] is used in a mathematical proof of some kind, thus making it the largest number used in a practical way. I'm not sure though.
NeoLogicification So it's the longest sequence of trees of length 3 under some conditions? Of course the numbers TREE(4) and so on exist, so what was done with the particular case of 3?
Wait...
The probabilities in a 7X7 Rubik's cube is a number larger than all the atoms in the Universe...
Mind. Blown.
Simply incomprehensible.
same
More than just that
_"in the_ *visible* _Universe"_
... there, fixed it for you.
Imagine the amount of atoms in all the possible universes where a different configuration set of that cube exists...
@@merek6986 Worse, imagine how many permutations there are in a universe that consists ONLY of tightly packed 7x7 rubiks cubes ; )
The largest number is me setting my microwave to popcorn mode
I love how fast the tree(n) functions are growing
all the steps you need to go trough to get Grahams number with the 3's and arrows and g1-g64. but with tree(3) you go:
tree(1) = 1
tree(2) = 3
tree(3) = stupidly big (makes Grahams number look like 1)
tree(4) = Impossible
@@spencerdumlao1654Fun Fact: Graham's number (TREE(3)) is TREE(4) times smaller than TREE(4) lol
*Look around for a moment*
...10
Maximillian Fox Dude, that's in base Loader's Number O.o
"Wow, look at those mattresses! There must be so many!"
"Wow"
"How many do you think there are?"
*looks around for a few seconds* "4."
Graham's number is so complex that people who use it in explanations still use the base of three. The can't even change it to 4 for variety....
The number exactly one integer bigger than any other number that has been named or is to be named in the infinity of all times and all spaces (and because of that it can have no name).
It is useful because it has an important role to always state the largest number, and it is not arbitrary because it has a clear relation to the second largest number.
And it's not a number because if x+1 doesnt exist then x is not a number and your system would require x=x+1 because all ever nameable numbers would be smaller
Imagine how big TREE(G64) would be !
ok, this is big! :D
Far smaller than scg (3), let alone scg(13), or loader number or big foot
Eric Arsenault which are laughably tiny in comparison to Oblivion or Utter Oblivion
@@rykehuss3435 Oblivion? Did you mean, infinity?
H i Nope. Oblivion and Utter Oblivion are real numbers. Infinity is not. Look them up. googology.wikia.com/wiki/Oblivion
infinity is not a number it is a term
+reflexlexus 676 Infinity is a category of numbers like Aleph Null and Omega etc.
+reflexlexus 676 Right. Omega is a number.
reflexlexus correct it is a made up "number" standing for a really big amount.
reflexlexus idea/size
reflexlexus that's some true ass shit right there.
Rayo([φRayo(10^100)](Rayo(10^100)) (φ defined as the Veblen function) (the Rayo(10^100) inside of [] is the level/subscript of the Veblen function) I call it the "Rayveb Constant" aka Reverb Constant.
That's what googologists call a salad number. Also, in the world of googology, this is not considered significantly bigger than Rayo(10^100). In fact, your number is going to be Rayo(10^100 + n) where n is the length of your defining string that must be added to the 10^100 symbols of the first-order Rayo's definition. The additional symbols represent instructions to iterate the function defined in the original 10^100.
Amendment -- I forgot that you included the Veblen function. So the added string must include the iteration instructions plus a definition of the Veblen function, if the original 10^100 don't already include one. Still, it's a trivial size when added to a google.
11:16 replace tree(3) with it, I was dying the whole time
I knew about Graham's numba from Numberphile's channel (grasping at it still makes smoke come out of my ears), I liked the vid and understand why the very large numbers become unexplainable without training. I would watch more videos similar to this fer sure!
The trivial way to make a number larger than Rayo's number is just to add one to it, or at one to the number of symbols being used ect. The non-trivial way would be to create a language more expansive than set theory.
And if you define a function which is X(0) = 1, X(1) = LBN, X(2) = GULBN, ..... keeping applying the same formula, how about X(GULBN) ?
2 to the 82,589,933 Power - 1 is the largest prime number we know.
Great video! I was never the best with mathematics but was always very interested in it. Your video definitely helped me to think outside the box a little bit and learn something new. Thanks!
I love this. I find it exciting, interesting, fascinating, and strangely enough, incredibly relaxing listening to your explanation!
I have a suggestion for the largest number. Tree of Graham's number worth of Primes. Or Rayo's number worth of Prime numbers.
No matter how big a number is, it'll always be closer to 0 than to infinity...
so true though
Graham's number is pretty big. But how about this:
I define F1 as G(G64), that is Graham's series for Graham's number.
F2 is F1(F1), which is G[G(G64)]. So that's Graham's series for the number F1.
F3 is F2[F2(F2)]
Imagine FG64, which is F, but instead of 3 or 4, it's Graham's number.
Now imagine I would write FF9. Which is F for the number F9. FFF9 is F for FF9.
Let's think of FFF...FFF9 and the 3 dots represent an FG64 number of Fs. And we call this number A1.
A2 is an A1 number of Fs.
My number is A64 (in honor of Graham's 64 from which I started).
Hey this is maybe the only time I've actually seen someone make a number that really is significantly bigger than Graham's number in the comments section. Let me see if I understand this correctly. F1 = G(G64), and FG64 = G(G(G...(G64)...)) with a 1 + G64 number of G's. Then A1 is FFF....FFF9 with FG64 number of F's. And A2 is FFF...FFF9 with an A1 number of F's. And then you have A64, which is Afilon's number. I'm trying to understand exactly how big this number is. Graham's number scores omega + 1 on the big number scale, which I'm sure about. FG64 would score about omega + 2. Then A1 would score omega + 3 I think, and A64 would score omega + 4. I'm not positive but that's what I think it is. This is in reference to something called the fast growing hierarchy. Omega is the first transfinite ordinal.
starrecipe9 I'm guessing TREE(3) is still larger, right?
Yeah, TREE(3) is very big. The TREE function grows very fast. It's really like the person in the video said. It grows so fast that it just doesn't seem like there is a lay man explanation for it. It is possible to understand what the TREE function is, but even once you know what it is it's not clear how fast it grows, and it grows much faster than you can imagine. The Googology website has some information on it, and they have a page on the Fast-growing hierarchy. You can learn about the fast-growing hierarchy on youtube, but searching for David Metzler's videos. He goes deeper and deeper into it for a long while, but never gets up to anything comparable to the TREE function.
Afilon G(Graham's number) = GrahamplexG(Grahamplex) = GrahamduplexG(Grahamduplex) = GrahamtriplexAnd so on with Grahamquadriplex, Grahamquinplex, Grahamsextiplex, Grahamseptiplex, Grahamoctiplex, Grahamnoniplex, and Grahamdeciplex.I'd love for this to get popularized.
I saw the FF and the digits, and for a split second wondered if someone was talking about Final Fantasy games, but then my nerd brain caught up with reality. Funny for a sec anyway...
-1/12 is the largest number as it's sum of infinite amount of numbers
***** 1+2+3+... actually has an answer and that is -1/12. There are plenty of proofs, either simple ones, relying on some already known sums of infinite divergent series or more rigorous obtained by means of complex analysis.
Sum of all naturals is in fact equal to -1/12, this is proven and there is no doubt that's true.
Michail Bialkovicz it's a divergent series, you can't sum it. Sorry
EDIT: changed convergent to divergent
***** Yes, sorry I meant divergent
ThisNameIsG It most certainly is divergent series and yet it can be summed, and that sum is -1/12. That is proven fact, there are proofs online, just google one, the fact you don't understand this and refuse to look for a proof doesn't mean this sum isn't correct.
Michail Bialkovicz Calm it with the accusations, read what I said again, digest it, and understand. Thanks
I came to a conclusion that you can count past infinity
№ is cardinal numbers it's basically infinity but different you see there's no other way to count past infinity but you can if you change the cardinal number to ordinal numbers it's basically the same but the ordinal number can overlap cardinal numbers which mean it can overlap infinity,but theres a common letter in ordinal number,(*)that is Ω if you put it at the end of infinity you can count past infinity it's Ω1,Ω2,Ω3 and so on and so on now for the other people who doesn't get it imagine a line a infinite amount of lines imagine putting a line in front of the infinite amount of lines so what goes past infinity (read again to understand,read where the asteris is)
gg, you discovered Wainer hierarchies
Well explained.
After googol my brain was just like: "big number @.@"
+Job Koppenol Yeah, he lost be at "before".
I found it all pretty cool, i just wish he had been able to explain Rayo's number
Wait... He said a googol is 1 with 100 zeros next to it... Technically that is kinda wrong... Because then it would be like this: 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Maybe I forgot or added a fe zeros but u get the point
P.s. This is a true joke XD
+Rickson Geometry Dash
That number you typed is one.
Rayos number + 1
*OWNED*
+Austin Cain XD. Wait... why do all the people have koala's faces
?
+Red Stone idk
Rayos' number to the arrow notation of royos' number. Suck it
+Austin Cain Rayos number^1 - .rayos = 1
.rayos is like:
if x69 is 12345
then .x69 is .12345
+LazyElectron +1 :P
Technically it’s rayo,s number because it’s the highist number even known plus infinty
Nah, it’s Sam’s number. It’s indescribable.
This was the very first your be video I ever watched!
Wow, I think this is a much better explanation of arrow notation than the one on numberphile. Definitely going to watch more of this channel.
The largest number is 6000, the same age as Earth
+CxSism LoL
LMAO
Ummm... its 4.6bil years old
Luka Waland This guy is an obvious troll, so just ignore this comment.
rly
how old are you
If you define numbers by starting with 0 and counting up, the largest number is -1. No matter how you reach this number, no matter what the characteristic of the field you try to define, it is the first number where, if you try to add 1 again, you reach a number that you have already defined, and thus you have already defined all the numbers that you can define in this way. Thus, my answer to your question is -1.
If you want to learn about the use for this definition, read up on 'two's complement'
The biggest number ever: how many times I have to rewatch this to get the slightest idea of what they heck they’re talking about.
9:16 I actually AM on a toilet lol
EWWWWWWWW
@@JoseGarcia-vt8mo i mean you need to all to things to survive so when you're the toilet for you so it's just natural to go ON A FUKIJGGH TOILET WHAT AM I DOING WITH MY LIFE
JustATest 01 umm...
Me going to fix
“I mean living things need to poop, if a living thing didn’t poop they would get constipation and die...” After that I don’t get what your saying :|
Lol it sounds like a good poop XD
R/youngpeopleyoutube
How about that: Rayo's number--->Rayo's number--->Rayo's number--->...Rayo's number...Rayo's number--->...Rayo's number) where the chained arrow notation is repated RAYO'S NUMBER times and you call that a R(1). Then you repeat it except Rayo's number is replaced by R(1), and you repeat the process R1 times. That is R(2). Then you make the same process over and over again until you get R(R(R(R(R(R....(R(Rayo's Number), and the amount of "R" 's here is R(Rayo's Number). That is TR(1). You after that repeat everything up there, except Rayo's number is TR1, and the "R(x)" 's are called TRn(1). You do that until TRtr(TRtr(TRtr(TRtr(TRtr(TRtr....(TRtr(TR(1)), where there are TR(1) "TR1" 's over there.
That is TRO(1). All above is repaten, until you will get TROtro(TROtro(TROtr(TROtr(TROtr(TROtr...|TRO(1) "TROtro"s later|(TROtr(TR(1)).
You repeat that^ again to TROP(1), then TROPH(1), then TROPHY(1) until TROPHYSTOLENGUYS(TROPHY(1)!!!!!!!!!!!!!|TROPHY(1) factorials later...|!!!!!!!). And that is called WIN(1). Repeat WIN(WIN(WIN... Well, you get the idea. THAT IS JUST WIN(2). Continue to WIN(WIN(WIN(WIN...|"WIN" WINS later|WIN(TROPHYSTOLENGUYS(1). That is called a WINS(1).
Feed WINS(WINS(1) to the tree algorithm, this is a Treerayo.
Feed Treerayo to the algorithm. G(G64) times.
That is the GTR(1) number or the GrahamTreeRayo(1) number. I need now my notation, the $ notation. When you do for example 3$3 all what are you doing is 3--->3--->3. 6$6=6--->6---->6---->6---->6---->6. 2$$2=2$2$2. 3$$3=3$3$3$3.
GTR(1)$$$$$$|GTR(1) $s later|$$$$$$(GTR(1)=GTR(2).
GTR(n)$|GTR(n) $s later|$GTRn=GTR(n+1.
GTR(GTR(GTR(|GTR(1) GTRs later|)GTR)=TheBiggestNumberICouldEverMakeInUnderAHour, or TBNICEMIUA
The smallest number bigger than any finite number set in a expression in the language of set theory
with a TBNICEMIUA symbols or less.
If you can beat this WITHOUT using any of my comment I am proud.
Why don't you write it in a standard form
That is FRIGGIN IMPOSSIBRU.
Mariomario3425
The smallest number than any finite number set in a expression in the language of set theory with D^RN (where RN is rayo's number, D^RN(RN^TREE(3)->RN^TREE(3)->RN^TREE(3)->RN^TREE(3)...->RN^TREE(3)) symbols or less.
D(k) is where D(k) is the sum of all possible bit strings described by the first k expressions of the calculus of constructions, and there are (RN^TREE(3)!)^D^5(99) times chained arrow notated RN^TREE(3)s
I would like to say that we have broken the rules.
Sir, you are recursing the recursation of recursive recursive recursation. Hell I don't even make sense to myself.
Mariomario3425 I propose a name for some of the numbers.Rayo(googol) = Rayo's number, as we all know. ThenRayo(Rayo's number) = RayoplexRayo(Rayoplex) = RayoduplexRayo(Rayoduplex) = RayotriplexThen it also goes Rayoquadriplex, Rayoquinplex, Rayosextiplex, Rayoeoctiplex, Rayononiplex, and Rayodeciplex.I hope this idea actually becomes popularized. Because it follows the googolplex, googolduplex, googoltriplex. etc. pattern that we've had before.
9:14 Me to my friend just before a jumpscare on a Halloween night
Great video and really well narrated. Your the best.
Okay, here is some I get up with
a*a = a^2
a^a = a↑2
a↑a = a→2
a→2 = ...
... = a☺2
number equal to 3☺3
☺
Infinity (∞) is an ideal kind of number.
It is the ultimate concept (and it means *no end).*
That is why ∞ is equal to ∞+1.
There are infinite bigger than order infinites.
@@againandagain174 not really
There is no such thing as infinite value since infinity is more of a concept than it is a set number. When it comes to operations starting with counting then addition and so on you can have a set of operation which grow faster than any of the operation on the previous set but that's not really going beyond infinity so much as it's creating a new set of fast growing function.
i knew about the MIT contest that resulted in rayo's number but i never saw the 'poster' and oh man thas quality advertising
Imagine you could fit the entire infinite universe in a full stop, and then placed a number so unimaginable, so vast, so far beyond human comprehension and experience, that if we were infinite beings with infinite capacity for memory, we still could not begin to grasp it, and we could fit that into a full stop, and placed another number, which truly dwarfs the previous unimaginable number by a truly incomprehensible magnitude...ad infinitum, we would still be finding numbers that made the previous numbers seem like dust on a pinhead in comparison...
I can't decide if I love the video or the comments more!
Hello you have reached customer service, my name is Sharkee, how may I help you?
Have I provided a satisfactory explanation of the world's largest number in a timely and courteous manner?
Then there is TREE(4), which is so big, you could say its about TREE(4) times bigger than TREE(3)
4:00 Also; who knows, you might be able to beat googol, with the number of all elementary particles (protons, neutrons, electrons, photons, Higgs bosons, dark matter particles (whatever those are), etc.), in the observable Universe. Or even just atoms, in the *_WHOLE_* Universe. 🤔
this is so educational thnx i enjoyed
oh wow
Great video! I was disappointed that there was no explanation of TREE(3), I've always wanted to learn more about it.
From 12:00-13:00 there wasn't really any information, but otherwise enjoyed it!
Also, Utter Oblivion is much larger than Rayo's number.
All numbers beyond Rayo's number are only extensions of Rayo's number or ill-defined. And meaningless.
It's Ill defined so it doesn't count. If it does count, then Croutonillion should be your answer as the biggest Ill defined number.
Infinity is NOT a number, it is the name of a concept meaning that numbers go on forever and ever. For example: Googol, Mega Googol, Centillion, Googolplex, Googolplexian, Skewes's Number, Moser's Number, Folkman's Number, Graham's Number, TREE(3), Loader's Number, Rayo's Number, BIG FOOT, Little Bigeddon, Sasquatch, Hollom's Number, Oblivion, Utter Oblivion, Sam's Number, and still son on!
So this Number is gonna be based off
The Knuths Up Arrow Notation as it is:
- Level 0: Counting (+1)
- Level 1: Addition (+)
- Level 2: Multiplication (×)
- Level 3: Exponential (^)
- Level 4: Tetration (^^)
- Level 5: Pentation (^^^)
- Level 6: Hexation (^^^^)
So let's start off with 2^5 = 2 × 2 × 2 × 2 × 2 = 32, 2^^5 = 2^(2^2^2^2) = 2^(65536), 2^^^5 = 2^^(2^^(2^^2^^2)) = 2^^(2^^(65536))
2^^^^5 = 2^^^(2^^^(2^^^2^^^2)) = 2^^^(2^^^(2^^(65536)))
HBUN(1) = 2^^^^5
HBUN(2) = 2(HBUN(1)^)5
HBUN(3) = 2(HBUN(2)^)5
Tip: Keep going on and on until you reach
HBUN(100) = 2(HBUN(99)^)5
Note: HBUN means Hector's Binary Upper Number
Function: HBUN(C) = 2(HBUN(C - 1)^)5
Size: This number is way bigger than G(64)
Whats your name?
I would say the largest number would be the number of different ways the entire universe could have unfolded to its current space and time since the big bang. If since the big bang even single quark or neutrino or even a string particle behaved differently than it did before, it would have resulted in a completely different universe. How many different possible combinations could have resulted to this current moment in time starting from the big bang?
And to come up with a larger number would just be calculated at a future time, because the number you could calculate at that time would be smaller than the number calculated a second later.
I believe I'll call this Riketz's number.
I belive it would still be smaller than, say, Graham's number.
such a number actually exists, it's called the "promaxima". look it up on googology wiki if you want.
***** it is
Riketz well if you go full physic then when you try to approach the "biggest" number, you will always get infinity. Let's say "the number of universes that has different physical constants than our universes", that will instantly give you infinity because ANY number could be choose, not to mention in modern physic there is 11 dimension so...yeah, just go with infinity and be happy would ya :)
Riketz He already mentioned that number, 10^10^16. The number of distinct configurations of the universe. Much smaller than a googolplex.
What about TREEfiddy
Googol:im the biggest
Googolplex:hold my plex
Graham's number:abe salo
Rayo's number: tom ho 0
Garden number: Abe
My number snn: 0's
I'm surprised one of them didn't just write down Aleph Null
They should have mentioned a rule that I see would have put a major wrench into Rayo's Number..
Rule: The number should be calculable, if it does not have a calculation it will not count
Rayo's Number is not a calculable number, there for Graham's Number is the biggest number... In the calculable sense.
I think you mean to say that Rayo's function is not calculable, because any integer is theoretically calculable. There is certainly some program that outputs Rayo's number, even though such a program would require close to Rayo's number of symbols to achieve such a feat.
Malachi Wadas Perhaps there's a slight difference between something being calculable and something ever having the possibility of being calculated.
Theoretically all the numbers are calculable because they have valid methods of getting a result, the only reason why we can't get the number is because in the physical universe the numbers are far bigger than anything in the universe.
***** Yup.
It's worse than just that. The universe is not stable enough to calculate these kinds of numbers. Expecting a machine to finish calculating the base-10 digital representation of Graham's number, even if it is supplied with endless energy and memory, would be like expecting a pencil balanced on its tip to stay standing on its tip for the duration of a trillion year hurricane. Our universe appears stable because it is relative to our lifespans, but on timescales of Graham's number of years our universe is an unstable fluttering mess of statistical fluctuations, in which even the most intuitively improbable events occur frequently.
If you have a hotel that is infinite, you start out with 32 people, then infinite people want to book a room their, then you just start at 33 and keep going it's not that complicated
But it doesn't start with 32 people. There's an infinity symbol in the top right corner.
The point of the paradox is to show how bs infinity is I guess.
A hotel with 100 rooms could only have 100 guests. A hotel with infinite rooms could always add more guests because infinity+n equals infinity still. And if infinite amount of new guests appeared, the hotel could still have them because of their infinite rooms.
The paradox comes when you go "oh, but all rooms were already taken!!! How can they receive more guests?" well, because infinity makes no sense. The issue is not trying to accommodate all the infinite new guests (as your comment implied), but trying to make sense of everything. If all rooms were already taken, why were we able to add more people? Well, because infinity makes no real world sense.
The thing is that the hotel is never really full of guests because that would imply infinity minus infinity equals zero (aka no rooms available). But you can change all current guests to even number rooms, which would give you an infinite amount of empty odd number rooms, allowing you to receive all the new infinite guests.
It's a perfect example of why you can't treat infinity normally.
The largest number is the number of days we're still gonna be in quarantine.
Well the thing about arrow notation is it only labels a tiny handful of the numbers, all those numbers near it need bazillions of digits to label correctly. Who has time for long numbers?
for some reason, my first thought when hearing about graham's number was "i wonder if graham's number could be written on all of the atoms, in all possible instances of the universe?" >_>
anyone got an answer to this?
sess not possible
sess yes the answer is no, even with Placnk length
i have an answer:
maybe
The observable universe is around 10^185 cubic Planck Lengths. That's all we have to work with.
Nope, not even close. YOU COULDNT EVEN WRITE OUT A GOOGOLPLEX, AND G(1) IS BIGGER THAN GOOGOLPLEX^GOOGLPLEX GOOGOLPLEX TIMES!!
Did anyone else try looking up Tree(3) online but ended up not understanding a single thing about it? lol
NUmberphile recently did a video describing TREE(3) at a level most people could understand, it's worth a watch.
This video should get at least 50 million or more views!!
I can definitely show you a bigger number, and one which you're familiar with because you've used it. but also one which you've never seen or thought of, because you were specifically taught not to think of it correctly.
consider how limits work. when we say something like: lim x->0+ 1/x = pos inf; this means that we are finding a value as close as possible to zero from the positive real side, and then plugging that in for x so that we can evaluate 1/x. in this specific case that value closest to zero yields infinity as its inverse, which means that it is infinitesimal. however, what if we break apart the limit operation into its base operations:
lim x->n+ f(x)
1) L(n) -> finds the closest possible value to n that is not n
2) evaluate f(n)
now, if we only take the first part, and apply it twice to 0, we'll get the second closest value to 0, whose inverse will necessarily be finite. thus, L(L(0)) = finite. but it gets better than this, because the first value we worked with, L(0), must be the fundamental unit of any number space, which means that L(L(0)) is exactly L(0) away from L(0), but also that 1/L(L(0)) is exactly L(0) away from infinity. further, L(L(0)) = 2*L(0). so 1/(2*L(0)) is the largest possible finite value, since doing anything at all to grow it larger results in hitting or exceeding 1/L(0), which is infinite.
we can clean things up a tad more by saying that L(L(0)) = L^2(0), which lays a nice foundation for distinguishing limits which approach from the right and those which approach from the left, since an approach from the left can now just have a negative exponent. for instance:
lim x->0- 1/x = neg inf
1) L^-1(0) -> finds the closest possible value to the left of 0 and assigns it to x
2) evaluate 1/x, resulting in negative infinity
thus:
1/L(0) = positive infinity; notice that we evaluated this
1/L^0(0) = 1/0 = NaN; this cannot be evaluated, and is thus distinct from 1/L(0)
1/L^-1(0) = negative infinity; notice that we evaluated this and it is distinct from both of the above
and this clears up essentially all of the paradoxes associated with limits, because those paradoxes only appear if you assume that the limit is evaluating at the stated value, rather than maximally close to it. but, evaluating at the value is impossible, which is why limits are invoked in the first place, and one of the most common places for limits to be invoked are at discontinuities where we know already that there is no value for the point, so... it seems like only idiots would be confused here. and yet, it is common for people to say that 0^0 is undefined due to the fact that it is an indeterminate form... despite the fact that it's trivial to show that anything to the zero power is 1, since the exponent indicates the number of times 1 is multiplied by the base, so if the exponent is zero then the base is utterly irrelevant to the evaluation of the thing. and thus obviously 0^0 = 1 if you have even a trivial grasp on what exponents are.
now, if we set up our number system such that L(0) is our unit, or in other words we define 1 = L(0), we end up with the number system that Peano thought he devised in what became the 'foundation of mathematics', but didn't actually. this is because L(0) is the one true successor to 0, so Peano's successor-function-based definition of numbers only works correctly if 1 = L(0). but, division does not work with these numbers, because L(0) is fundamental, and thus indivisible. and a consequence of insisting that 1 be divisible is that L(0) and 1 become completely decoupled and L(0) is now not a definable subdivision of 1, which is the property which renders L(0) infinitesimal in such a number system.
this is because L(0) must evenly divide every possible subdivision of 1, but if we allow 1/2 and 1/3, we need 1/6 to unify them, but that means we need 1/4 and 1/5 as well, and introducing 1/4 means we need 1/12 to unify it with 1/3 and 1/6, which further means we need 1/7, 1/8, 1/9, 1/10 and 1/11. and if we set those aside for a second and come back to 1/5, well to unify that with 1/12 we need 1/60, which means we also need 1/13, 1/14, 1/15... to 1/59. so the problem grows worse and worse every time you solve a piece of it. and this isn't even the half of it, since this unending process can only give use the rationals, which are a minority of numbers. the irrationals pose another problem entirely, because now L(0) must equally subdivide not only all of the rationals, which we just showed is not something we can handle mathematically, but also all of the irrationals at the same exact time. this does, however, tell us very clearly in two different ways that L(0) must be irrational.
thus L(0) is truly special, and 1/(2*L(0)) is also truly special, since it has properties you never even knew were possible despite it being right in front of you ever since you learnt about limits.
note that my number +1 is infinite. it's by definition impossible to have a finite value larger than 1/(2*L(0)). and, if this value can be expressed in first order logic (which, I don't think it can) then it would render the definition of Rayo's number a paradox. which is super fun.