Can you think of a bigger number than this?!
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- čas přidán 7. 12. 2023
- In 2007, a legendary battle occurred between two philosophers, Augustin Rayo and Adam Elga, where a new number was created. A number so large that if any human could truly imagine it's size, their head would immediately transform into a vast black hole (I am not kidding).
Rayo's number breaks the limitations of mathematical functions and even the English language to create something truly unfathomable! Even the Busy Beaver function stands NO CHANCE against Rayo's number!
In my last big number video, a lot of people beat my biggest number but I guarantee that no one will be able to give me a number as big and as well defined as Rayo's number!
Good luck!
So... I add a 1
Too smart 😆
@@jazlearn5147he’s got you there
I change that one to a factorial
@@Ilikewooper I think you win. Here is your trophy 🏆 😀
I add one to that factorial
One must imagine busy beaver happy
This comment is gold. 😂
The funny thing is, that there are infinitely more bigger numbers than the biggest number which we can accurately define.
If you picked a number truly at random then it would almost certainly be larger than Rayo’s number.
How would you pick a random number?
@@Juguitosdemora close your eyes and choose
@@davidyoung2990 It would be a 100% percent chance that it would be bigger than the Rayo´s number
@@IlIlIlIlIlIlIlIlIlIlIlIlIl1123yes and no, there is negative numbers too
Loving that I’m getting small creators in my recommend that aren’t fed off of goldfish attention span viewers
Sameeee
Corrections: 11!!!!! is 5 single factorials iterated, not double factorials;
BB(n) usually refers instead to the number of steps until halting; the maximum _total_ number of 1s (consecutive or not) is known as Σ(n). Recently, Σ(6) has been found to be far larger than 10^10500 -- in fact, it is tetrational level.
Also, nice to see the bounds on Rayo function being presented here lol, in fact in the large numbers community I was the first to suggest bounding explicit values for Rayo, although I did not participate much in the process. The first bounds were pretty bad, at around Rayo(1000) > 65536.
Correction: 11!!!!! Is 1 quintuple factorial iterated. 11!!!!! Is 66.
What a great video! Im so glad you made this one as these were the two functions I was having trouble understanding the most.
Anytime! Feel free to voice some more video ideas that you would like to see if you want! I'm glad I could help!
I couldn't really understand numberphile's explanation, so this is useful.
@@marty2035 Glad I could help!
@@jazlearn5147explan f10(10) (10) (10) or largest garden largest number
brilliant video! had me hooked not just because of the awesomeness of the content. well done. thank you
I'm glad you enjoyed it! 👍 😁
great video!!! Good job making the animations and speaking all the information clearly for me to understand!
Thanks! 👍 😃
amazing! thank you for answering my request. The visuals make everything easier to understand, I applaud your efforts, sir!
It's SO interesting that the result of BB(4) can be counted on hand while BB(5) is astronomical even for computers!
Anytime! If you have any other requests, feel free to voice them 👍
The Busy Beaver function is probably my favorite! If you look into it a bit deeper, you see that the reason computers can't find a value is because there is an astronomical amount of different instruction card combinations, and for each combination, you can't stop the beaver until you know it has finished or if it looping. This is hard because there are cyclic patterns that make it look like the beavers' movements are looping, but they aren't.
It's an amazing computer function and crazy to think about with googol Instruction cards!
Very interesting indeed. The busy beaver function is actually uncomputable, though! Meaning that you cannot compute the value of BB(x) for any x with one program, even with infinite time. This is because turing machines are equivalent to our computers, and so you could imagine a contradiction similar to Berry's Paradox if you could compute the value of BB(x) with one program.
Say, if you have the amount of states that you need to construct that turing-machine as x, you could make an x+y+1 (for some relatively small y) state turing machine which will start with every cell of the tape at zero, use y (here you can imagine why y would be relatively small: if it wasn't, BB would be slow growing!) states to set up the number x+y+2 (encoded into whatever encoding for numbers the x-state turing machine for computing BB uses), then x states for the BB program, and finally that one extra state to move right until it finds a zero, and then set that zero to one (if it's state z, then this would be 1->11z, 0->110) to increase the number. This would give us BB(x+y+1) > BB(x+y+2), which is impossible. This argument is slightly handwavy, but there is a very closely related problem known as the halting-problem with formal proofs.
Please note that this is different from one program existing which computes the value of BB(x) for some fixed x, which obviously exists: it's just the winner of BB(x).
Now... how was BB(4) computed? (and how is BB(5) currently being computed?)
Programmers can write "deciders" which will take a turing machine as input, and either say that it definitively doesn't halt or that it doesn't know whether the machine halts or not. Now we just have to make deciders which are strong enough to decide every four or five state turing machine, and then run the ones that it doesn't know about until the machine halts. Practically, you can't really know whether the decider is strong enough, so you just have to run the turing machines until a stronger decider comes along that says it doesn't halt.
Currently, a large project focused on this is bbchallenge (at bbchallenge.org)
@eig5203 very interesting. For BB(1), there are only 64 different cards to analyze, so surely this is computable??? Couldn't you do this with a pen and paper ?
@@jazlearn5147 Yes, that is essentially running a decider yourself instead of using computers. Once you get into something like BB(800) (I believe the current lower bound is BB(748)), then there aren't any deciders which will provably (in ZFC) work for all turing machines of that size. Eventually, every (recursively-enumerable) axiom system will run into this problem.
BB(5) is probably just 4098. BB(4) = 13 isn't as easy as counting. it was actually really hard to prove that every turing machine with 4 states which took longer than 13 steps to terminate, didn't terminate at all. same with BB(5)
It’s cool you gave context on that paradox, I find that interesting. I suppose he got around it by just describing it using second order set theory.
It's very interesting. Yes, that is how he overcame it!
Very interesting video! I’ve known of Rayo’s number and its story for some time now, but the paradox has somehow escaped me until today. Thank you for the information!
Thanks! There is a lot more I could have said as you probably know, but I didn't want to make a 40-minute video! Lol
Extremely interesting and Well made video, you deserve way more subs
Appreciate YOU! 😁 💛
The biggest number is 32,767. 16-bit signed integers should be enough for everyone.
2:09 bro, this is how a Turing machine works
Indeed it is! Busy Beaver function is a Turing machine!
Woah this is such an amazing video! So glad I found this, I really learnt a lot.
Thank you! 😁 I'm glad you enjoyed it!
I loved this video! Liked and subscribed
Thank you! 😊
Such an interesting video! You earned a new sub. Do you have any other videos about big numbers?
Thanks! Yes, I do! There is one about Googol, Googolplex, Grahams Number, and TREE(3), which are HUGE numbers, but nothing compared to Rayos Number.
@@jazlearn5147can you do USDGCS_2(k)?
Great video!!! Just wondering, how does Rayo’s number relate to Graham’s number or Tree(3)? Which is the largest?
Thanks! 👍 Grahams Number is the smallest of the three, then the next biggest is TREE(3), and then Rayo's Number makes both those numbers look like 0 in comparison! The Busy Beaver function fits in between TREE(3) and Rayo's number 👍
The magnitude of Rayos' number is uncomprehensible. It's BIG!
but what if i lets say take Tree(googleplex)^grahams number factorial
@extazy9944 I would say Rayos number is bigger, and I would guess the busy beaver function of a googol to be bigger. These numbers are massive!
@@jazlearn5147 what about tree(busy beaver)
@@extazy9944rayos number is bigger than tree(tree(tree(tree…(tree(googolplex^grahamsnumber!) with tree(3) nested trees
Thinking back to another video I watched, considering they said you can put any number into the TREE function, we can always have "TREE(TREE(...TREE(Rayo(10^100)...)" but in order for that to be the largest number it has to at least be proven finite.
The same can most likely be said for the Rayo function as well, there is no limit to how big a number you can put in there so long as said number is finite; it will still come nowhere near close to the smallest form of infinity (Countably infinite). And then we have to explain to the kids why infinity is not a number and just means something that continues on without bounds...
TREE is finite for all finite inputs, so that is indeed finite.
And of course the same thing can likely be done with the Rayo function by stacking its own function within itself (i.e."Rayo(Rayo(Rayo...)")@@hyperpsych6483
We know TREE(n) is always well-defined (finite) because of Kruskal's tree theorem. Kruskal is basically the reason any of us are ever even talking about TREE(3) in the first place.
wtf is TREE
dude did u even watch the video? dont comment if u dont know shit@@matheuscabral9618
Great video !!! Well done. Your explanation was easy to understand
Your channel is far too underrated!
We are on the come up! 😁👍❤️
0:58 I'm confused by double factorials. Also, many single factorials get bigger than a few double factorials.
(((3!)!)!)!
= ((6!)!)!
= (720!)!
= (2.601*10^1746)!
@-wvy_ Yes, single factorials do get bigger, but due to the way it was written on the board, we must use double factorials. I was confused at first as well, but that is what every source that I looked at said.
@@jazlearn5147 What are your sources even? Because I found an interview with Augustin Rayo on the Math Factor Podcast, which tells a completely different story:
Rayo starts by writing a 1. Then Elga writes down as many 9's as he can fit on the board. Rayo counters by writing as many 1's as he can fit on the board, which resulted in a much larger number, because he could fit way more digits of 1 on the board than Elga's 9's. Then Elga changes all except the first two 1's to factorials, clearly resulting in a bigger number.
There was no mention of double factorials whatsoever.
@@melooone when you write many factorials, the sources I looked at said they become double factorials. As for the other slight inaccuracies, I did that for the video sake. Didn't want it to be too long. It was more to introduce the numbers, not so much to be historically accurate.
So... we factorialize it so, (Rayo number)!
🤯
This video was way better than Tony Padilla’s explanation on numberphile. I understand rayo’s number now but I still don’t get busy beavers but that’s ok
Rayo's number to the tetration of Rayo's number = 💀
Crazy MASSIVE! 🤯
rayos number to septation of rayos number and double factorial x rayos number
beth 2. I know some would argue it's not a number, but I hope this does count. I loved your video, so I have subbed!
I haven't heard of that one! 😀 I'll have to look into it! 👍 Thanks for the sub!
Beth is transfinite.
You can’t just say “infinity” when someone asks you for a large number.
@@diht that's why I said " I know some would argue it's not a number", I wouldn't consider it one, but in some ways it can be viewed as one.
@@ZephyrysBaumI would say that the Beth numbers are numbers since they describe sizes, with Beth numbers describing the sizes of Infinities. I think what needs to be established is that a number must be finite since you could just chose a Rank-into-Rank Cardinal, but that’s meaningless since most people don’t know, nor will know how those numbers are defined
@@blightborne6850 They will know if you explain it to them. But Beth numbers are the starting point to studying Strongly Limits. If you want more info, I could talk to you more about that in Orbital Nebula server.
I'm curious to know why you chose to describe Rayo's first comeback to be ((11!!)!!)! when using five single factorials would have been much, much larger. Do you have a source that implies Rayo definitely intended the string of characters to refer to double factorials as opposed to single factorials? For example, you show that 11!! Is equal to 10395. But 11! (Single factorials) is equal to 39,916,800 all on its own! Is there a convention that says all two factorial marks together are assumed to be double factorials? If so, was that a convention that Rayo would have followed? Great video, covers these topics clearly without needing any deep mathematical understanding.
Yea. At first I did that because I was using Wolfram Alpha as my source, which told me to do it like that. But then I realized it was an ai source and thus did not fully understand what I was doing 😆 so I looked at single factorial values and the numbers would have gone off the screen real quick (because they are so big!), so I just decided to introduce double factorials for fun while keeping the numbers on the screen lol 😆
Fair enough. I tried doing my own back of the napkin math using Sterling's approximation to find the value for single factorials and the resulting power tower is a nightmare to try and simplify. Thanks for the clarification! As a very, very handwaved simplification of the real value, I got the tetration of 10 to 6, or 10⬆️⬆️6 using up arrow notation.
@connerwinder2218 Thank you! 👍 😊
a↑ⁿb=a↑↑↑...n...↑↑↑b
rayo's number to the power of rayo's number
Yup. You win 🏆 😆
this is funny " and pulls out the bizzy beaver of a googol. "
Y E S!
I call it plank number, Plank^10^100(10^100), because, its probably in a "superposition" between being finite and transfinite, lemme tell how it works:
take the largest possible salad number that can be made in 10^100 steps or less, call this number P(1).
Now take the largest possible salad number that can be made in P(1) steps or less, Call this number P(2).
Repeat the process 10^100 times.
That's plank number
PLANK^10^100(10^100).
Very interesting!
This has a definability issue (in that salad numbers aren't conclusive) but it's kinda funny to see somebody make a function which actually uses salad numbers so nice i guess
bro had enough
lets surpass
f_ΒΗΟ(PLANK^googol(10↓↓3))?&PLANK^googolplex(TREE(3)) where ? is from the number BIGG
Kid named Nuclear Engine:
well, yes i can. rayo's number + 1
Damn! 😆
RAYO NUMBER×2
RAYO NUMBER^2
This is underrated
I’m more interested in this random video than the entirety of my Math 3 class that I just had an EOC on and idk why 😭
Also if there was some kind of function to determine the digit count of any number (including decimal places), you could just take a repeating decimal like (1/3) and multiply it by itself when plugged into that function, and you now have an infinitely high value
Since I have no sense of how big that is: I will explain what I think of as the biggest number. It uses tetration, but even further along. The number idea was basically a googleplex to the tridecation of a googleplex. tridecation is basically exponentation, execpt instead of multiplying the base the amount of times specified, you do that many of the base to the dodecation of eachother. Dodectation is pretty much the same. I would label them 13 (tridecation) and 12 (dodecation). If you label them as 13 and 12, exponentation is 3. (Multiplication is 2 and additon is 1)
Well, now imagine that, PLUS ONE
What you described is not even a quark compared to rayo's number, or even to far smaller numbers such as Graham's number and TREE(3).
Check out Knuth's up arrow notation. What you've described is a Googolplex (11 up-arrows) 2. Also using a googlgolplex becomes unnecessary, just use 3's instead and add 2 more up arrows to ensure it's larger.
@@blackeyefly I was going to say that the Graham sequence is larger than this.
I'd argue that the FGH would imply tree(3) is also larger than rayos number
@@jazzabighits4473 I don't think that's correct, surely you can define the TREE function with far fewer than a googol symbols of set theory
Nice explained. What about Large Number Garden Number? I am not mathematician, but according to articles on the internet, it should be much bigger than Rayo's number.
Yes, it is indeed bigger but I am pretty sure it is not as well defined as Rayos Number.
lol i came here just to comment this :D
@@jazlearn5147 ironically, googologists consider Rayo's to be ill-defined and Garden well-defined.
@@jazlearn5147 It is much more well-defined than Rayo's Number.
@@jazlearn5147 in googology, lngn is accepted as the largest well-defined googolism and rayo is actually ill-defined according to googologists
i mean a google search would tell you lngn is a larger well defined number but adding one works too
So i make it Ω..
Thing is you can literally always go bigger because you can always just add 1 to whatever number is came up with, no matter how unfathomably big it is because by definition that number would be bigger.
in the rules of the battle it was stated that you can't just use the opponents ideas and build on it, each new number has to be a unique concept
Well what about infinite?
By definition infinite = infinite+1
@@wolfVFV Exactly the point I was making!
@@wolfVFVinfinity is a concept, not a number. kinda like how your virtual AI girlfriend is not a real woman either.
@@wolfVFV Infinite is not a number, adding number 1 into infinity is like adding 1 into an apple it doesn't make sense
1:18 The notation extends beyond double factorials to multifactorials. 11!!!!! isn’t ((11!!)!!)!, it’s 11 * 6 * 1 = 66.
Is that actually how it works? I looked at a lot of sources, and it said the way I did it was right. Your way makes more sense, tho 😆 you are probably right. Thanks for the knowledge!
@@jazlearn5147 The number of exclamation marks is the number subtracted for each multiplication. Five exclamation marks means that the multiplication is 11×(11-5)×(11-5-5)...etc. As it happens this stops neatly at 1. In other cases, we would stop before things go to zero or below. The keyword here is "multifactorial", and Wikipedia has some information about it if you're interested.
Interpreting more than two exclamation marks as a combination of double and single factorials is what the WolframAlpha website does - which might be what you used(?) - because it hasn't been programmed for triple etc. for some reason.
It's not entirely certain, but in context I think the 11!!!!! on the blackboard during the competition was intended to be ((((11!)!)!)!)!. Stacking single factorials like that gives the largest possible result. There's also that 66 would have been a losing move.
I always assumed it meant ((((11!)!)!)!)! And since 66 < 1111111, I'm sure so did they. Just shows the importance of defining your functions if you're using them in an obscure way rather than assuming everyone is on the same page.
@19t2000 Yes, I believe you are correct in that assumption. I made a mistake.
add one to that and i'm the winner now
Note that its impossible to compute busy beaver function for values bigger than (i think) 6. Well never know more than 6 values about our precious function
Correct!
The Number TREE(3) is bigger than grahams number(g63) so how big would TREE[TREE(G63) ] Be?
It's smaller than Rayos' number but huge. I don't think anyone can comprehend the size of Rayos' number. By using set theory language, you can go beyond anything you could imagine!
@@jazlearn5147 Ayo What about (Rayo's number)^TREE(Rayo's Number) ????
So, the thing about this is that Rayo's number is not truly calculable, you would have to go through literally every iteration of the google characters to find it. In some cases it wouldn't even be considered a number, but many say it is without realizing that there is no direct formula to the value.
sure it's nearly impossible to say anything about it but so is tree(1000) using your logic and most people would say is a number even though people can barely say anything about it so it is a number just a completely useless number
Uh, so is many other "large numbers" (even, say, TREE(3)). We have no way to even find their last digits, let alone first digits, but they are considered numbers. Also, someone has made a 7901 character Rayo script which exceeds BB(2^65536-1).
So it is computable. You found a way to compute is. True, doing so in the real world is a tad impractical due to the amount of computer time required - but that's a small matter. It's finite, it's computable, it's just big.
all three of your first three replies are basically saying the same thing
@@vylbird8014 No? the rayo-string was constructed set theoretically and proven to be able to output a larger number than S(2^65536-1).
A RayoPlex, a number with Rayos number of zeros
MASSIVE!
the title: Can you think of a bigger number than this?!
me: just add 1
But Rayo's number just arbitrarily picks "a googol" as the "Rayo function's" input.
Graham's number isn't arbitrary because it was used in a proof. Tree(3) is a little arbitrary but using 3 as the input to describe this number is done because of how amazing it is that it exceeds Tree(2) by so much. Obviously Tree(4) is bigger still, but that doesn't "feel" as amazing to me.
But Rayo just picked a googol out of nowhere. I can easily beat that number with a bigger input. Rayo(Tree(googol)), for example. Rayo himself could have picked that input instead-he just...decided not to. His idea of a function was brilliant, but his choice of input doesn't "feel" interesting to me like Graham's number or Tree(3).
Well, too late. You can't add a bigger input because that would be breaking the rules, also get it "GOOGOLogy". fitting for the largest accepted number
It's the largest because the Rayo() function is the absolute fastest growing function defined in mathematic terms we have today
@@moahammad1mohammadfunction that is used by LNGN:
@@moahammad1mohammadlarge number garden number is probably bigger
Also little bigeddon is bigger
That’s definitely true. I suppose for the purpose of this battle it didn’t matter because there was an implied rule that each turn had to use a novel idea, so his opponent couldn’t use his own Rayo function against him with just a higher input. But yeah, I definitely agree, the number is arbitrary, but the function is pretty general.
I'm still waiting for a video that explains HOW we know one huge number is bigger than another huge number. I know (because I've been told) that Rayo's number is bigger than Graham's number, and Tree (3) is bigger than Graham's number, but how do mathematicians prove this?
a guy called harvey friedman wrote a proof of this statement in 2000
graham's number is g(64)
what's g(1) then?
well its just (NUMBER)↑↑↑↑↑↑(NUMBER)
and g(2) is (NUMBER)(G1 ↑'s)(NUMBER)
and i think you get the pattern there
On the fast growing hierarchy (FGH), Graham's number (or sequence) is equivalent to the function of ordinal omega or omega+1 (where 0 = successor/counting function, 1 = addition, 2 = multiplication, 3 = tetration......with infinity = "omega function", the next "strongest" function being omega+1) Graham's number sits between this level of function and the previous level, that is, its growth rate is 'omega', or faster than anything that can be described through any lower function (for example, you can't express graham's number as an exponent, or even as a tetration, or anything really less than its explained growth.
Eventually, after 1, 2, 3,..........infinity (omega), omega+1, omega+2, you get to omega times omega, then omega times omega times omega, etc. The whole time these are describing insanely fastly growing functions. In the end, there's some ridiculous ordinal called the Rieman Zeta ordinal or something like that, describing some ridiculously fast growing function.
The rate of growth of TREE(3) is higher than the Zeta ordinal.
However, I've still been able to explain the "strength" or growth rate of these numbers using just the English alphabet and a few symbols (numbers, brackets, equals signs, etc.), let's say 50 symbols at most right? Rayo's Number denotes a number that is so large that you need at least 1 googol symbols to explain it (rather than the 50 I'm using right now).
I'll look into that. I'm guessing it'll be very complicated mathematics, but I'll see 👍
@@jazlearn5147 The youtube channel numberphile explains it well, check oiut their extra footage video on TREE(3)
Rayo's number to the hexation of rayo's number😵
can you explain why double factorial is different than or the same as factorial of factorial?
It is different because you multiply every second number up to a given number rather than every number, thus making it much smaller. I was under the impression that in the actual Big Number Battle, they used double factorials, but it appears from further research that this was not so. They used single factorials.
Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
I don't even know what to say to that... it's definitely bigger, but I can't comprehend the size of that number!
@@jazlearn5147( tree (Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number To The Power Of Rayo's Number) )!
TREE(this)
IIRC the game had rules where they couldn't just say "that plus one" or "TREE(that)", because otherwise it would go on forever.
Must not have thought of Rayo's number + 1!!
rayo+1!2 < rayo^^^rayo
what if i multiply this number by one hundred trillion bullion million
Then it would be one hundred trillion billion million times bigger 👍 😁
ME: Let´s if your number is x, mine is x + 1.
That's called the successor function, and it's not necessarily a number. But I'll allow it 👍 😆
rayo's number to the hyperpower of itself
its exactly what it sounds like
Yes... Whatever the biggest number is that you can define or imagine, and then add 1.
i have a bigger number, whatever rayo's number is +1
The FINITY is bigger than rayo's number
Best explenation of Rayos number I've ever seen
Thank you!!!
Video: Rayo's number is the biggest number
Me: Utter Oblivion
The Infinity! in question (yes infinity isn't a number i know I'm just joking)
oblivion numbers arent well defined
Nice video animations.
Thanks! 👍 😁
All this to explain how strong a black flash is
I love it! :D
whatever number you say , plus one.
Smart move 👌
There's an Even bigger number than rayo's number And it's called oblivion And also utter oblivion
Absaloute infinity:HERE IS YOUR DADDY BOIS🗿🗿🗿
How are they able to compute the BB function? Do they just brute force it?
Well, we only really know up to BB(4), and to do that, they just run every possible program and hope it doesn't take 6 years to spit out an answer lol
I think the TREE function would have fit nicely into this video. I'm pretty sure it scales bigger than the BB function, and you can also do something like TREE(BB(10^(10^100))) (the tree of the busy beaver of a googolplex)
I have already made a video on TREE(3) so I left it out of this one 👍
TREE doesn’t grow faster than BB(n). The Busy beaver function is uncomputable, the TREE function is computable. (In fact, we have found it’s growth rate.)
@@SG2048-meta We have in fact not found its growth rate. The believed growth rate is the order type of a certain related set, but Irrational Arrow Notation proves that the growth rate is not always equal to the order type.
@@zswu31416yeah sorry for that mistake.
yes. in fact, i’m thinking of it right now.
Go on.
MyTime(10^1000) - The biggest number humanity will create/say in 10^1000 years
"remains one of the..." - no mention at all of the others or the largest defined (if there is one) - truly bush league - and I'm a welder
I think he meant single factorials
Although barely even considered a number, utter oblivion is the largest number I’ve ever heard of and possibly the largest finite number created
I haven't looked into that one yet. Sounds amazing! 😁
Bowers has some interesting ideas XD
ultimate oblivion
utter oblivion, oblivion, ultimate oblivion, etc. are all ill defined
croutonillion is the largest well defined number by virtue of having all ill defined steps replaced with a known well defined one, and it uses lngn extensions in its own definition
croutonillion is also the largest salad and finite number known, but its not the largest valid googologism because it is a salad number.
@@worldprops333 you meant the well defined version of it?
All of this high level mathematics in a video with a title that absolutely BEGS ME INCESSANTLY to respond with the words "your mom". WELL, I'M NOT GOING TO.
Wow i love this video! Is it not possible to do BB(Rayo(10^100)) or am i just dumb.
Thank you!
If you do BB(rayos number), you are substituting into the slower growing function. Even though the busy beaver function is the fastest computable function, the rate of increase of the Rayo function far exceeds it, so it would be best to do Rayo(BB(10^100)).
It's hard to know if your number is bigger than Rayo's number due to the sheer size of these numbers, but Rayo(BB(10^100) is definitely is bigger! 👍
@@jazlearn5147 ok i understand thanks!
Really hard considering Rayos function in FGH.
We dont know the placement of it but we know that:
if f_a(n) corresponds to it
Then a>all computable and writable countable ordinals (including but not limited to, the church kleen ordinal and all its counterparts, aswell as λ, the supremum of all writable ordinals)
We would have to define a REALLY BIG ordinal if we want to reach that growth speed.
absolute infinity:
omega:
any infinite cardinal:
The beaver is the turing machine
Not quite. The busy beaver is a specific set of rules on a turing machine
I added 10 more double factorials mixed with some !s for excitement
This is getting out of hand 😆 That number is MASSIVELY MASSIVE!
So just use the next order higher of symbol and define a function as the higbest definable thing in the order that the rayo function uses, then diagonlise and make the input the prder of set theory used.
Is this truly so? Which grows faster, BB or TREE? And do they ever intersect?
TREE(n) function goes 1, 3, and then huge. BB(n) remains small-ish up to 5, and then it becomes huge but probably wouldn't surpass TREE(n) until n equals 8 or 9. They do intersect, and BB grows faster overall.
i'm sorry but the face the red one makes at 0:47 is so funny i'm crying
I'm glad you enjoyed it 😆
You can always make a bigger number by adding 1.
The rules of the game were that you couldn't use naive extension such as adding one.
The formula to find a number bigger than a number is the number+1
It's a good formula 😆
The concept of a sequence is a loop without an end. The concept of ordinals is the idea that the sequence has an end, it just breaks mathematics so there is no point of proving it. No mathematics will ever be able to match it at all. You can try to produce something, but you are at 0 and the line marking the 0, no matter how small it is in your head, will not even be crossed.
Interesting!
Take that number and raise it to the power of itself
Nice, but I add one to that and win, lol. Nah, jk, you win 🏆
😢
@@arandomgamer3088 pentation it
TREE 3: "Hold my beer."
not even close 💀
You can define the TREE function using first order set theory in far fewer than a googol symbols. This means that Rayo's number must necessarily be more than TREE(TREE(TREE(TREE(TREE(...TREE(3)...)))))
I don't know exactly how far deep it could go but I know that I couldn't write it out. Even if I used every atom in the observable universe to denote another iteration of the TREE function.
Wait what i thought 11!! was around 10^39916800 can you explain to me where you found the double factiorial thing because i'm confused.
You're right. Double factorial is a different function and shoudn't be confused with using factorial twice. There is a mistake in the video
I know utter oblivion if that even is a number
utter oblivion ill defined
i take busy beaver of rayo's number.
The biggest number shows up in the scale where your mom stands
Love this 😆 🤣
Garden number prob laughing at this vid rn
just add a +1 to whatever the oppenent writes on the blackboard
fr
You have to be novel and create new unique ideas. That was the rule. 👍
yeah, that number times two!
BB(Rayos number). Checkmate
You win! 💯
Legends know that the biggest number is FOREST(3)
I think you meant TREE(3)?, from what I've seen yes it's an unfathomably large number, magnitude bigger than a number like that of the Graham's Number, but still pales in comparison to Rayo's Number, by a huge margin.
@@Vxrtu No, the joke is that a forest is bigger than a tree, so FOREST(3) is even bigger than TREE(3), because a whole forest is much larger than just a tree.
I just have a question, and if it's stupid just tell me: what about rayos number + 1? wouldnt that be bigger?
that was a part of the contest that he didnt explaine, they could use a technique that was used before so just adding a one to rayos nummber would just be using rayos technique.
but yes adding a 1 to rayos nummber would make it bigger LOL
Not a stupid question, the video maker just didn't include the important rule of "doing something new" when presenting a bigger number. That's definitely a bigger number and you could make an even unfathomably bigger number like Rayo(Rayo(10^100)), but it just uses the same function as before and is not a new creation.
Why would you double factorial 11, when 11 factorial would seem to be bigger, seeing as it doesn't skip the even numbers?
That is just how the notation works. You are 100 percent correct, tho. If we just took factorial each time, the number would be significantly larger!
@@jazlearn5147 So, if you do not use parentheses, the notation defaults to double factorials wherever possible over a factorial of a factorial?
@secret12392 Yes, that is correct 👍
@@jazlearn5147Bruh
Absolute Infinity
fish number
instead of using first order set theory, let's use second order set theory
and instead of using up to a googol symbols, let's use up to TREE(Graham's number) symbols (I could use something insane like Rayo(BB(TREE(Graham's number))) but i didn't want to repeat already used functions)
so basically the smallest number greater than any finite number that can be expressed in second-order set theory with TREE(Graham's number) symbols or less
ABSOLUTELY MASSIVE 🫡🤯
dare you to throw me in the ring
My bad 😆