Several quick notes: Yes, I am aware of SSCG(3) and Rayo's number but I thought that the video would drag on a little. There are several minor errors with the visuals. Specifically at 3:19 where it says that 65536 is 2 tetrated to 5 rather than 2 tetrated to 4 and at 6:31 where it shows TREE(10^10) when I say "TREE(googol)" when it should show TREE(10^100) When talking about graham's number, I said that g0 was 3 hexated to 3 but actually that's g1 and g0 isn't really a thing. I excluded infinity because I intend to make another video covering exclusively infinities. Sorry about the music being a little too loud. Edit: Yes, everyone. I am writing a script for a sequel. You can stop mentioning SSCG(3), Rayo's number, BIG FOOT, the fast-growing hierarchy, etc...
Infinity is an idea of something which does not have an end, not a number. That is another reason why no one should mention infinity as a largest number in their video about googology.
@@Nikewertz__ Precisely, though infinity does serve as a sort of sister mathematical branch to googology so one could still assume I would cover it, which is why I gave another explanation as to why it's not covered.
@@AGuideToInterestingStuff Also how are numbers that are as great as or greater than 10^1060 even usable, or calculatable? Because the highest number that computer systems can ever understand is 10^1054 after that going one value higher than that number will make the computer round it out to either "Nan" (which stands for not a number,) or the computer will round the number out to Infinity, So how did we even discover these numbers? 🧐🧐🧐🧐🧐🧐
I would 100% watch that Also a bit of unrequested feedback, the video was really great but the audio mixing was a touch off, I found it a bit hard at times to understand what you’re saying over the music. Just lower the volume of the music and maybe raise your mic volume a bit and it should be fine :)
Oh just make sure you don't slip in the puddle TREE(TREE(g45))^^^3 miles from here, we accidentally knocked over TREE(TREE(TREE(TREE(60^^^^^^^^g69))))^^^^^^^^g64 bottles of water, each containing TREE(g64) ounces of water each
Sure, just go to aisle TREE(TREE(TREE(TREE(g65)))) and make sure you don’t knock over the newly made section, it is still under construction and you will be get a TREE(TREE(TREE(TREE(TREE(g(g(g(291))))))))$ fine for breaking it, and also that’ll be TREE(g(20572))$ hexated to a googolplex sir
Rayo’s number gets mentioned a lot here, and I would like to bring up some fun properties of Rayo’s function used to construct such number The function grows linearly when the input value is small: with 10 first order set theory symbols you can write 1, with 30 you can write 2. Seems slow right? This is not the case however as it grows faster. By 300 you have the function growing at the rate of multiplication, by 340 you have it grow at the rate of exponentiation, and by 400 the rate becomes tetration. And we’re not talking about the actual value of Rayo’s function; no, this is just a lower bound. If I remember correctly, RAYO(380) is at least greater than 2^65536 By the time you reach 7400, Rayo’s function grows so fast that it is almost certainly possible that the value is greater than S(2^65536-1), S() is a function that is growing faster than ANY COMPUTABLE FUNCTION, faster than G, faster than Tree, and so on And Rayo’s number has the input set at a googol. The number would certainly be so big that the number would not only lose its meaning, but any number or symbols or machines that can enclose an iota of its being will certainly collapse into a black hole, for there isn’t close to enough information to store the concept of Rayo’s number
I was thinking of mentioning Rayo's number, actually but I felt like the video was getting too long. Same story with SSCG(3). As for infinity, I actually have an entire sequel planned about different infinities.
@@jasonzawtun LNGN (Large Number Garden Number) is a number that was meant to be the largest number, but it is ill-defined so Rayo's Number is the largest "defined" number.
Wholly underrated... I expected it to have a couple of thousands of subscriber with all of those transitions and hooking me into thay content. Those demonstrations were also on point. I believe you'll have a very succesful career in RU-vid in the near-future, given such pristine quality of work os assured. There are some mistakes here, you have mentioned them in the comments yourself, but, hey, people learn from mistakes. A master has made a multitude of more mistakes than the beginner has tried. You got this. Edit: Oh yeah, the music was fire too, very on-spot music that goes with the video.
The thing I like about TREE is that you don't need ANY underlying mathematics beyond early grade school to understand the rules unlike pretty much every other 'big' number.
I mean 1000000 isn't too hard to grasp as a 1920x1080 screen has a little over 2M pixels. But this video did make me realize how big a googol (as well as googolplex 'n googolplexian) actually is
I'm a little bit disappointed that you didn't go into the limits of computation in such a video. There are functions out there which are equal to a certain number but it's unprovable what number they're equal to.
4:40 actually TREE(3) is the biggest number that was used in any mathematical proof (for Kruskal's three theorem), Graham's number is just more well-known
Oh, that's an excellent question. There are lot's of good ones but I'm going to have to go with the old favourite: Phi. I feel like my answer might vary from day to day, though.
I'm so curious about this TREE(3) number that I often search the internet for a page/picture where every tree is drawn that can be made. I still haven't found anything.
Unfortunately, there are more possible trees than there are plank lengths in the observable universe so we couldn't possibly list them all, but you can always try with a pencil and paper and draw your own trees. It's quite fun, actually.
@@AGuideToInterestingStuff I bet it would be fun, if I understood the rules. I understand the ,,Nth tree can only have N seeds" I understand the ,,trees can't contain previous ones" but no matter how many videos I watch about this I don't understand the common ancestor rule.
@@rngesus66 My apologies, allow me to attempt to explain it again because, you're right, I think I might have done a bit of a lackluster job in the video. For one tree to contain another, you don't really need to understand the common ancestor rule, simply imagine taking out parts of the tree. If we had a simple straight-line tree that went A--B--B then we couldn't make one that was A--B--A--B because we could remove the second A to make the first tree. I find that that's the most helpful way to think about it.
Since you asked so kindly: You are using the lowercase tree function, not as fast growing as the uppercase tree function or TREE function. Since irrational numbers don't work with tree, those letter Is in "Irritating" along with all the other letters. This could be rewritten as tree((3i)2r)(2t)ang) In all seriousness though, a passive aggressive comment probably isn't the best way to get a person to listen to you. Instead, try respectfully pointing out the issue, it's crazy how much nicer you come across.
sick video! the music was pretty cool also at 3:15, don't power towers work by working out the highest power first instead of the lowest, so instead of 2^2^2^2^2 = 4^2^2^2 = 16^2^2 = 256^2 = 65536, it would be 2^2^2^2^2 = 2^2^2^4 = 2^2^16 = 2^65536 ≈ 2×10¹⁹²⁷⁸? i could be wrong, but this is a way more way of interpreting power towers to make much bigger numbers lol anyway, nice video once again, i liked the narration 👍
Thanks very much and thank you for pointing out that mistake, you're 100% correct. I think what happened is that I accidentally put 2 tetrated to 4 rather than 2 tetrated to 5 but, by a quirk of the maths, it comes out to equal the same as 2 tetrated to 5 if you calculate the power tower from the top. Thank you again for your kind words and for discovering that error which is now mentioned in the pinned comment.
yeah can i also get SSCG(308)^^^TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(3) cups of coke
The world of numbers starts with one! What should I do with it? can it be used in game creation codes? Have you seen what is on the clock? After 12 comes 1, there are also "units of time" like: minute, hour, day, and someone else knows: second. But what's next? After all, the day does not go on indefinitely, they only repeat themselves. A MONTH! What's it? And yes, this is again a unit of time, if you add up 12 months, you get a year, and out of 100 years there will be a century, I'll tell you that people on average live 74 years at the moment. So what are we going to do with such a small but useful unit? the number "two" is a new universe, numbers begin after it, even hundreds, even thousands, but there is a number and more... I present to your attention... A million! This number is not so close to infinity, but even far away, people in the 17th 18th 19th 20th century invented a bunch of numbers, some of them are even difficult to pronounce, if you thought that infinity is a number, then no, it's not a number, because you can't count up to this number, and don't try, even with God it won't work, it seems you have a question "why did you come up with infinity?", everything is simple, people couldn't make a normal number and made your infinity, and then we have many more questions. Chapter two. Multiplication, division, numbers to a power, tetration. What are we going to do with the numbers? And I'll throw the chips in the trash so that some homeless guy eats the chips. So what about the numbers, and the scrambled eggs? I ate the scrambled eggs, but the numbers are fine. No jokes. Did you know what multiplication is? We learned this at school, how much is 2+2? If you said 4, then you are right, but how much is 9×6? well, of course 54, it's not difficult, but here are the following questions... Pull the notebook out of your pocket, but why do you need a notebook? How much is 2 in a Cube? Viewer: of course it's eight! Me: that's right, but how much is 6^3? Audience: 216, easy! Any more questions? I'm out of thoughts... Chapter 3: The Mafia. Hey, hey, fool, what kind of mafia? What kind of control is this? Who put the mafia in here? I didn't seem to play it, some kid is looking at me, what are you doing here? Child: and I have a *mate* on you, do you know what the mafia is? Mafia top. Me: then I'm *mate* again, I don't care about you. You fool. Mafia of that, sports pillow. mafia... Chapter 69420: The Mafia is the best. I'm saving you right now... chapter, not chapter; 9292291. You're going to die! Roll the dice! Child: so what? Wait, no! *disappear* I finally got rid of the kid, phew.
uncountable infinity is theoretically infinite cause.. where do you start? 0.0000001?, 0.00000000000000001?, 0.000000000000000000000000000000000000000000001? and even if you reach the next number, you have to do it again and theres no limit on how many zeros there can be
Just letting people know numbers like big foot and sasquatch and the big garden number cant be visualised compared messed with or calculated even with supercomputers they are not big numbers they are not huge either they are virtually impossibly big and would shrink multiverses into black holes that are unfathomably big and that is not even close to the lower bound of their sizes.
I just don’t understand how the function TREE produces finite numbers. Like, it just doesn’t get in my head, I don’t understand it. They should be infinite right?
It is confusing because it definitely does seem like it would be infinite but there is a proof that shows otherwise. The idea of the proof, if I understand it correctly, is that the maximum tree size only grows by 1 but at the same time the amount of trees you're not allowed to make is also growing. Eventually you'll have made every single tree possible that doesn't contain another. I totally get what you're saying though because it really does seem like it should be infinite.
Unfortunately, that actually doesn't get very far. To get a number larger than even something like Googolplex, you would need more 9s than there are atoms in the observable universe so it's a little impractical. Also, I think the video would have been a little boring if it were only 9s.
3:06 I don't even have to do the math to know that 2 to the tetration of 5 is WAY more than 5 figures. I still will, though. 2tet2: 16 2tet3: 2^16=65536 See?
Hexton 3^tree(tree…}tree(tree…}tree(10^^^^^^^100^^^^^^^9999^^^^3377)^1,000,000,000,000,000,000,000,000,000,000,000(decillion) By: RU-vidr Wolfingtoniii8720 the Arch Duke of the Kingdom of Puppi Island(this is how it’s spelled).
very cool video, love your editing style. This video seems a little bit simular to math genius. I do admit you did make the video more entertaining, but you might need to check if your video is original or not.
Thank you! I hadn't watched the video before you mentioned this but, now that I have, I see what you mean. Rest assured that I will graciously take the video down if Digital Genius requests.
@@AGuideToInterestingStuff Yo! Thanks for replying :) I'm not on digital genius's team or anything btw, i just watched both the videos pretty close together. All good, and great video :)
if you know... 1 stud needs about 0 seconds to climb it. but THAT breaks the rule because you didnt climb IT, so, only 3 studs or more is allowed, but, what if ITS negative? you will fall. -1 and more is allowedd also... how many seconds does it need to climb TREE(3) studs?
Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by Tree(graham's number) tetrated by a whole lot.
As stated in the pinned comment, I didn't include any more numbers simply for the sake of time and having a consistent 'narrative' so to speak that raps up at a good point.
