Today, we learn the story of Graham's Number. My Website: day9.tv/ Me on Twitter: / day9tv Find me on Facebook: / day9tv Fancy Day[9] Swag: day9.tv/store/
Hey Sean, no idea if you'll read this, but on the off chance you do: thank you so, so much for this video. I first saw it when I was in high school, and it inspired me to go on and major in math in college. During undergrad, I really wanted to take graph theory and combinatorics because of how interested you made me in discrete math from this video, and I fell in love with the subjects. In fact, I'm actually doing some research in Ramsey theory right now, which I was introduced to here. I applied for PhD programs over the past couple of months, and I know now for sure that I'm starting my PhD in math this fall, where I want to continue studying combinatorics and graph theory. This video changed my life in an amazing way. Thank you again.
Day[9] either wanted to make a lecture on this number and put the joke in at the end, or he started by brainstorming the most epic "yo mamma" joke possible. I have to believe it was the latter.
+SwenglishGamer He explains it worse and even makes errors. eq. 4x3 is 3x3x3x3. And with grahams number also was he discribed as G0, thats actualy G1. G0 is 4. You Form G1 out of 3 (G0 times up-arrow notation) 3
I watched this video for the first time a couple years ago. Since then I've taken a calculus course, and the E^2X joke is now the funniest thing in the world to me.
derivative of e^x is e^x. Derivative of e^2x is 2e^2x, differentiate again and you get 4e^2x. Basically if you have a function f(x)=e^g(x) its derivative will be e^g(x) * g'(x)
Ha, this is great, I took discrete math for CS with professor graham a few years ago, he didn't bring up grahams number until the day before the final and then everyone realized who he was.
Theres no g0 in the definition, the first term is g1=3||||3. Either that, or if you take g0=3||||3, then you should go up to g63, not 64, other wise you end up with a number that unimaginably dwarfes the actual Grahams number.
Henry14arsenal2007 well again, he mentions that in grad school he didnt even look at his grades. Ergo, it's safe to assume based on his claim that he missed that part... Sure g63 must be a massive number, but g64 must be even greater... technically in this vid, Day9 just created a larger number than graham's number. xD
2 year old comment, but apparently g0 is accepted as 4 for some reason. A minor error on Day9's part (or maybe a tremendous error?) but g64 is still a bit large.
There are an infinite number of numbers, so technically speaking most positive numbers - integers to make it easier - are bigger than Graham's number. If you ignore integers, then it's a matter of degrees of infinity and I will leave that to the experts.
Calculus was actually my favorite high school class. I love physics so learning about the mathematics that made understanding physics possible was the most interesting thing to me, even more than my physics class. I love the ability you gain to understand physics when you learn about derivatives and integrals, and it's definitely the class I took the most away from so I just love hearing about these things that I'll learn about when I go into higher forms of calculus.
I'm a graduated aeronautical engineer (24 years old here) and I have never seen these up arrow notations before. And believe me I was pretty dedicated in college. We don't really need these notations in engineering, since we never really work with numbers or that magnitude. We actually reach for the opposite side of the story, we learn to work with really small numbers due to Finite Elements Methodologies. Each field of science has its own specific beauty about it.
To express exponential notation. It takes a number like 4x4x4x4x4x4 and comprises it simply into 4^6 which is much easier to display and type into a calculator/computing system. It is used a lot in technical fields that have to understand exponential growth and decay.
In terms of Googology, graham's number is actually quite small. It's only f(omega+1,64) in the fast growing hierarchy. To make a truly large number, let's start with a set S containing (0,1,omega,Omega) where Omega is a extremely large undefined ordinal. The set C(0) is defined as the set S closed under addition, multiplication, and exponentiation. Psi(0) is the smallest ordinal not contained in S. This is equivalent to an infinite tower of omegas or epislon_0. C(1) is the set C(0) U epsilon_0 closed under addition, multiplication, exponentiation. Psi(1) is the next ordinal which is an infinite tower of epsilon_0 or epsilon_1. In general Psi(a) = epsilon_a. But the function gets stuck at zeta_0 because psi can only build finite epsilon nesting. Here, we inject Omega into our function to unstuck it. Now, psi(Omega +1) would be the first epsilon number after zeta_0. The function continues this way being unstuck by Omega everytime a system runs out of steam. Ex. Psi(Omega) = zeta_0 psi(Omega^2) = eta_0 psi(Omega^Omega) = Gamma_0 psi(Omega^Omega^omega) = the small Veblen ordinal. This continues until psi(epsilon_Omega+1) where the function get stuck permanently. We can now denote psi_1(0) as equal to epsilon_Omega+1 and insert this into our original collapsing function and denote Omega_2 as another large undefined ordinal that will unstick our new function. We can continue with psi_2 psi_omega and even nested psi's. So imagine if we denoted alpha_0 as the fundamental sequence (psi(0),psi_psi(0),psi_psi_psi(0)...) then plugged this into the fast growing function and added a one to recurse it into itself f(alpha_0 + 1,3). This is a staggeringly large function. Much larger than tree(3) and scg(13) but smaller than the BB functions and rayo's number. The latter are uncountable and uncomputable.
Within the first couple of minutes, you blew my mind. I'd always known that you could color every state in the U.S.A. with four colors, but I'd never known you could do it with any map. I quickly tried to disprove it, and quickly failed. I'm not a math major, but you definitely made me think on a critical level that I haven't experienced in some time. Thanks :)
I started recursively copy and pasting 9^9, which turns into 9^99^99^99^...^99^9 And for some reason, ctrl+v happens faster than holding a key down. I have no idea why.
This was one of my favorite videos of all time (both really educational and funny), until the end. Now, it is, without any doubt, the greatest youtube video ever. I'm laughing so hard that I'm crying in the resteraunt where I'm getting lunch, and a family of 4 is staring at me uncomfortably.
+Phatnaru0002 This doesn't really make sense. For it to make sense, you'd need to add a number behind the second g. Like g(g(1)). As g1 is already unimaginably big, and you have to do the process where you take the previous g value g1 times, it's more or less too big to even explain. If you then scale it up to g(g(64)), you can't really do much with it, except go "whoa, that's a big number", as it is way to large to imagine. You could do the process infinitely if you want to, always adding a new layer of g's. An example could be g with g64 g64's of arrows.
gudpeter100 are you being serious or are you just joking, because I know how to make a black hole, although I don't know how to preform the task of doing so
Kylan Andreychuk If you had an atom for every digit of G stored in memory, and you had all these digits stored in the universe, the density of the universe would pass its Schwartzchild Radius and the universe would collapse in to a black hole.
Actually Day9 it was seriously narrowed down recently in a massive advancement for the field of mathematics, proving that the solution is actually somewhere between 7 and Graham's Number. With specifics like that we're sure to figure it out exactly sometime between now and Graham's number years.
Hey Day9, just wanna say I've seen Ron Graham actually explain his number and arrow notation; I couldn't understand his own explanation of arrow notation because it was too incoherent. Then I saw you describing it. Thank you for making this. Lol
Graham's number is one of the most interesting things I've learned about. I've been subscribed to Numberphile since their beginning, fantastic channel.
I have watched this video every few months now for like three years and it is first now that I can relate to the type o guy who talked about the really curvy lines and enormous polynomials haha
Serious Day[9], if you ever get tired of doing a gaming channel, please consider an educational channel, maybe? I learned more from you about notation than my first Trig class
I studied engineering at the University of Washington. And for a Technical Writing class I made a presentation on the Mandelbrot Set and its relation to Julia Sets... My presentation may have been poor, but I thought it was awesome until I looked up and saw everyone in the classroom was bored. Talking later with other 4-year engineering students at a prestigious university, not only did no one think Julia Sets were fascinating, no one even knew what they were.
Well, most engineering students hate math so It's not really surprising. When I talk about how much I love math and talk about the extra maths technical electives that i'm planning on taking my engineering peers just ask me "why would you take extra math?".
So tell me more about determinants in pascal's triangle. "Oh god yes! Day9 has prepared me for this moment! And Starcraft, but I'll save Starcraft for later."
I really love math! I'm not that good at it but I think it's very beautiful. Two years ago I spend a whole year doing calculus (just lower classes because I never got it) and after really putting effort into it I got straight A's in all my writing and oral exams. I know that compared to the amount of math problems and ways it's not difficult but I never imagined that I would actually appreciate sitting down and differentiate equations before going to class.
Fun fact: that 4 color theory was the first proof that used a computer to prove it. They came up with a number of graphs (as in dots with lines connecting them) and just fed it into the computer to brute force it. It was controversial when it came out (of course) but obviously once everyone warmed up to computers it was accepted (and retested I assume).
I made a picture testing it out, and it worked easily. None of the same color touched. I used Red, blue, green and yellow. The middle was red, then the ones outside starting from Northwest (A), heading east in a circular pattern and ending up just south of A, went yellow, blue, green, yellow, blue, green.
THANK YOU DAY 9 I heard of a number so big you cant imagine it and couldnt find it but wanted to tell my friends about it and know it do not only know that it was Grahams Number but i can just show them your video!
If you want some perspective, Vsauce does an episode on 52 factorial, and 52 factorial is about 3^7625597484935 times smaller than 3(Double Up Arrow)4 that he was talking about at 11:00
![Day[9] Story Time #5 - A High School Crush](http://i.ytimg.com/vi/CdLnuGAPNUg/mqdefault.jpg)
![Day[9] Story Time #5 - A High School Crush](/img/tr.png)
![Day[9] Story Time #6 - Trying to be healthy](http://i.ytimg.com/vi/xNuA_gEgtr4/mqdefault.jpg)
![[Highlight] Why PvZ in Broodwar is WEIRD](http://i.ytimg.com/vi/oM3Z7FjuixU/mqdefault.jpg)
![Day[9] Story Time - How I Almost Died](/img/1.gif)
I watch this video every few years and it never fails to destroy me xD
Same lol
same
Now was the yearly watch.
8 years later and I’m still watching these laughing lol. Such a good sense of humour.
Hey Sean, no idea if you'll read this, but on the off chance you do: thank you so, so much for this video. I first saw it when I was in high school, and it inspired me to go on and major in math in college. During undergrad, I really wanted to take graph theory and combinatorics because of how interested you made me in discrete math from this video, and I fell in love with the subjects. In fact, I'm actually doing some research in Ramsey theory right now, which I was introduced to here. I applied for PhD programs over the past couple of months, and I know now for sure that I'm starting my PhD in math this fall, where I want to continue studying combinatorics and graph theory.
This video changed my life in an amazing way. Thank you again.
Did you get your doctorate?
Late response, but this is so effing awesome!
Day[9] either wanted to make a lecture on this number and put the joke in at the end, or he started by brainstorming the most epic "yo mamma" joke possible. I have to believe it was the latter.
Those 17 minutes totally paid off at the end.
Day[9] needs to be on Numberphile
Day 9 needs to own numberphile
+Popo Sandybanks Day 9 is Numberphile.
You do realize they had the man who came up with this number talking about it on Numberphile?
+Miister Cloud Day9 is more entertaining is better
+SwenglishGamer He explains it worse and even makes errors. eq. 4x3 is 3x3x3x3. And with grahams number also was he discribed as G0, thats actualy G1. G0 is 4. You Form G1 out of 3 (G0 times up-arrow notation) 3
I've literally seen this video at least 10 times and it STILL gets me every time at the end there. Christ, day9
Was that 17minute build up to a "yo mama" joke ? 5/5.
5/7 would watch again
*G* out of *G*
Day9 should become a teacher. His students would literally have the best math class in the world.
did Day9 spend over 17 min educating us just to crack a yo mamma joke? i like to think so and its awesome.
I watched this video for the first time a couple years ago. Since then I've taken a calculus course, and the E^2X joke is now the funniest thing in the world to me.
Jake Thornton Explain! Explain! Or you will be exterminted!
Pff and now it's been two years since I took calculus and I don't remember shit from it :P
haha
derivative of e^x is e^x. Derivative of e^2x is 2e^2x, differentiate again and you get 4e^2x. Basically if you have a function f(x)=e^g(x) its derivative will be e^g(x) * g'(x)
I come back every six months or so to relive one of the sickest burns I've ever witnessed.
5:43 I died at the e^2x joke XD
Rip
Did Day9 just spend a quarter of an hour teaching us some experimental math, just so he could drop the worlds best yo mamma joke?
Ha, this is great, I took discrete math for CS with professor graham a few years ago, he didn't bring up grahams number until the day before the final and then everyone realized who he was.
Wow! Coming back and seeing this at the end of the decade, 2019. Amazing how much Sean has changed, and is yet very much the same.
Now that is the best "yo momma" joke ever
17 minute buildup to a mom joke. Has to be in the top 5 mom jokes of all time
10 years have passed and this is still my favorite video of all time.
"I want you to think of the biggest number you can think of"
The Busy Beaver function with Graham's number as its argument.
WHERE IS YOUR GOD NOW
Boo-yah! And thanks for sending down a multi-hour rabbit hole learning about Turing machines!
Ackerman(TREE(G64),TREE(G64))
Large Number Garden Number: pathetic
I just watched a 17 minute set up to a your mama joke. I'm not sure how i feel about this.
+Matthew Szubelak i wish i could have seen the chat for this
You ruined the fun....
I physically applauded.
Not like "i'm clapping for real right now"
I actually clapped for real, just now.
day9...i wish you were my math teacher in high school
Theres no g0 in the definition, the first term is g1=3||||3. Either that, or if you take g0=3||||3, then you should go up to g63, not 64, other wise you end up with a number that unimaginably dwarfes the actual Grahams number.
Henry14arsenal2007 well again, he mentions that in grad school he didnt even look at his grades. Ergo, it's safe to assume based on his claim that he missed that part... Sure g63 must be a massive number, but g64 must be even greater... technically in this vid, Day9 just created a larger number than graham's number. xD
+Henry14arsenal2007 you can make a arrow lol ↑
2 year old comment, but apparently g0 is accepted as 4 for some reason. A minor error on Day9's part (or maybe a tremendous error?) but g64 is still a bit large.
I think he may have said that because he does programming and indexes should start at 0.
@@uknownada My initial thought was that g0 should be 4, because if g1 = 3||||3 and g2 = 3(|*g1)3, then it follows that g1 = 3(|*g0)3 therefore g0 = 4
This number doesn't even come close to the debt I owe after college.
Also, the format of how the up arrow affects the thins after it makes my brain very happy.
Literally the greatest thing I've seen in possibly my whole life.
Ronald Graham of Graham's number just died this week and made me remember this old day[9] video. Thanks for spreading your enthusiasm for math!
But almost every number is bigger than Graham's Number!!!
Though that's technically true, you can also argue that any number is tiny.
There are an infinite number of numbers, so technically speaking most positive numbers - integers to make it easier - are bigger than Graham's number. If you ignore integers, then it's a matter of degrees of infinity and I will leave that to the experts.
i watch this every couple of years, still great
My brain hurts so good
I saw this video when it was first published and 9yrs later the yo mamma still gets me everytime
6:10 Jokes on him because I was thinking of TREE(3)
Calculus was actually my favorite high school class. I love physics so learning about the mathematics that made understanding physics possible was the most interesting thing to me, even more than my physics class. I love the ability you gain to understand physics when you learn about derivatives and integrals, and it's definitely the class I took the most away from so I just love hearing about these things that I'll learn about when I go into higher forms of calculus.
StarCraft related question; if G64 is Graham's number, what's GG?
It's when you keep going with g65, g66, g67... all the way till gg0
gg is basically infinity then^^
or divinity?
Apparently it's extremely hard to comprehend considering nobody in Bronze League ever mentions it
I'm a graduated aeronautical engineer (24 years old here) and I have never seen these up arrow notations before. And believe me I was pretty dedicated in college.
We don't really need these notations in engineering, since we never really work with numbers or that magnitude.
We actually reach for the opposite side of the story, we learn to work with really small numbers due to Finite Elements Methodologies.
Each field of science has its own specific beauty about it.
Funny to think he actually talked to Brit about this when they started dating xD
Best setup for a "yo mamma" joke ever. But, seriously, this is just as informative and even more entertaining as the videos by Numberphile
Thanks for 5:45 mate. I jokingly used it as a pickup line on a girl who's crazy about math. Shit worked surprisingly well. We're currently dating.
Did it work so well that you are still together?
To express exponential notation. It takes a number like 4x4x4x4x4x4 and comprises it simply into 4^6 which is much easier to display and type into a calculator/computing system. It is used a lot in technical fields that have to understand exponential growth and decay.
I think I saw the Numberphile vid on this and I think you explained it quite well. - Nicely done :)
I saw a different vid on Grahams number, I think it was Numberphile but can't remember
In terms of Googology, graham's number is actually quite small. It's only f(omega+1,64) in the fast growing hierarchy. To make a truly large number, let's start with a set S containing (0,1,omega,Omega) where Omega is a extremely large undefined ordinal. The set C(0) is defined as the set S closed under addition, multiplication, and exponentiation. Psi(0) is the smallest ordinal not contained in S. This is equivalent to an infinite tower of omegas or epislon_0. C(1) is the set C(0) U epsilon_0 closed under addition, multiplication, exponentiation. Psi(1) is the next ordinal which is an infinite tower of epsilon_0 or epsilon_1. In general Psi(a) = epsilon_a. But the function gets stuck at zeta_0 because psi can only build finite epsilon nesting. Here, we inject Omega into our function to unstuck it. Now, psi(Omega +1) would be the first epsilon number after zeta_0. The function continues this way being unstuck by Omega everytime a system runs out of steam. Ex. Psi(Omega) = zeta_0 psi(Omega^2) = eta_0 psi(Omega^Omega) = Gamma_0 psi(Omega^Omega^omega) = the small Veblen ordinal. This continues until psi(epsilon_Omega+1) where the function get stuck permanently. We can now denote psi_1(0) as equal to epsilon_Omega+1 and insert this into our original collapsing function and denote Omega_2 as another large undefined ordinal that will unstick our new function. We can continue with psi_2 psi_omega and even nested psi's. So imagine if we denoted alpha_0 as the fundamental sequence (psi(0),psi_psi(0),psi_psi_psi(0)...) then plugged this into the fast growing function and added a one to recurse it into itself f(alpha_0 + 1,3). This is a staggeringly large function. Much larger than tree(3) and scg(13) but smaller than the BB functions and rayo's number. The latter are uncountable and uncomputable.
Well duh, I coulda told you that when I was 5.
yo day 9 , when you were a math major how many times did you get asked if you were going to teach?
I'm at 23.
Well I am only 15 years old and asked at least 50 times. I win.
you are a math major at 15?
Graph theory, number theory, counting, and geometry are the best parts of math in my opinion. So much fun.
Fucking see?! This is why Sean doesn't get supply blocked.
The pixeled Triforce shirt is amazing.
when h said yo mama i fucking died.
Within the first couple of minutes, you blew my mind. I'd always known that you could color every state in the U.S.A. with four colors, but I'd never known you could do it with any map. I quickly tried to disprove it, and quickly failed. I'm not a math major, but you definitely made me think on a critical level that I haven't experienced in some time. Thanks :)
You should teach Math. I would fly 3↑↑↑↑3 miles to sign up for your class.
This is by far the best video on the entire internet. And it will be on top, even if there's graham's number of videos out there
I would love to listen to this guy talking about math in a podcast!
The numberphile video about Graham's number was good. But this... you have taken it to the next level.
The numbers of times you have to date girls for find your future wife is between: 1 and Grahams Number. So dont be sad. It will happen^^
that makes me feel better Kappa
hahaha! nice one
Idk why more people haven’t seen this. It’s such a great video for learning obscure math facts
I thought i was being smart by imagining 600 googolplex, but... holy shit.
I started recursively copy and pasting 9^9, which turns into 9^99^99^99^...^99^9
And for some reason, ctrl+v happens faster than holding a key down. I have no idea why.
Ferrohazard And then you pressed "=". R.I.P. computer you were a good friend.
Oh, no, I put it in notepad. Then I just looked at it. It was kinda like Hitler from Inglorious Basterds. "NEIN NEIN NEIN NEIN NEIN!"
Ferrohazard
LOL
I have been waiting for story time all week!
That some sort of mathturbation.
This was one of my favorite videos of all time (both really educational and funny), until the end. Now, it is, without any doubt, the greatest youtube video ever. I'm laughing so hard that I'm crying in the resteraunt where I'm getting lunch, and a family of 4 is staring at me uncomfortably.
So how big is Gg?
+Phatnaru0002 This doesn't really make sense. For it to make sense, you'd need to add a number behind the second g. Like g(g(1)). As g1 is already unimaginably big, and you have to do the process where you take the previous g value g1 times, it's more or less too big to even explain. If you then scale it up to g(g(64)), you can't really do much with it, except go "whoa, that's a big number", as it is way to large to imagine. You could do the process infinitely if you want to, always adding a new layer of g's. An example could be g with g64 g64's of arrows.
It was a joke... ya know "GG!"
6 years later this is still my favorite joke on RUclips.
Isn't 3||||3 supposed to be g1, not g0? That makes a pretty big difference. (How big? Bigger than yo mamma...)
This is true, but in both cases, g64 is retardedly big
That comment just made my life complete. I can now die happy. Thank you, sir, here is your nobel prize.
pretty sure that 3||4 already has more digits than particles in our universe
Number of particles in the universe: 2^80, so you are correct
How could we have possibly measured the particles in out universe, when the light from most of the universe hasn't even reached us yet?
*****
It is of course an estimate of the particles in the observable universe and the estimates varies.
Ok, so, only the observable universe, meaning that we could very well have more particles than that.
Are you worried we don't have enough? :p
I love math too! I'm a math major as well. This video really hits home with me. I love it. :)
My goal in life is to calculate this monster using a computer
Kylan Andreychuk The consequences of doing so, if it ever would be possible, which it won't, would turn your computer into a black hole.
gudpeter100 are you being serious or are you just joking, because I know how to make a black hole, although I don't know how to preform the task of doing so
Mustache
Kylan Andreychuk Too much information in a confined space would inevitably form a black hole. Nothing more, nothing less
Kylan Andreychuk If you had an atom for every digit of G stored in memory, and you had all these digits stored in the universe, the density of the universe would pass its Schwartzchild Radius and the universe would collapse in to a black hole.
"But math isn't just used for the torture of small children"
Haha, laughed my coffee right outta my nose
Math S.
Is a contraction of the word MathematicS
Math is what a catholic with a lisp attends on Sundays.....
Its MATHS ...MATHS.... MATHS....
ty day9, just made my day so much better
What if we did graham's number.... to the power graham's number...
That number is dwarfed by simply going to G65.
julian villaruz but i counter with my G66!
Chris Werth I beat all of you with G(G)
LOL the GG has spoken! O.O
You would get a meaningless number.
Actually Day9 it was seriously narrowed down recently in a massive advancement for the field of mathematics, proving that the solution is actually somewhere between 7 and Graham's Number. With specifics like that we're sure to figure it out exactly sometime between now and Graham's number years.
thank you for not doing the typical youtube choppy video editing. wish you had talked about the motivation for coming up with Graham's number though.
Hey Day9, just wanna say I've seen Ron Graham actually explain his number and arrow notation; I couldn't understand his own explanation of arrow notation because it was too incoherent. Then I saw you describing it. Thank you for making this. Lol
Graham's number is one of the most interesting things I've learned about. I've been subscribed to Numberphile since their beginning, fantastic channel.
I saw that mama joke coming from a mile away...very nice, my hat off to you!
17 minutes to bring it to a yo’ mama joke! Not to mention a math joke that ‘I just keep getting bigger’ earlier. I love this man.
I've never understood Graham's number before. This was fantastic. You're a wonderful teacher. I have to send this video to all my math friends!
Podcast for story time. This needs to happen!
I have watched this video every few months now for like three years and it is first now that I can relate to the type o guy who talked about the really curvy lines and enormous polynomials haha
I love you, and I love day[9] story time. I'm watching this over and over again. More math and more stories!
So I think it math teacher when I was in collage was fan of yours because he told this same joke, the same way you did. Hahaha great math lesson.
Honestly Day[9] is the best storyteller ever
Serious Day[9], if you ever get tired of doing a gaming channel, please consider an educational channel, maybe? I learned more from you about notation than my first Trig class
I studied engineering at the University of Washington. And for a Technical Writing class I made a presentation on the Mandelbrot Set and its relation to Julia Sets... My presentation may have been poor, but I thought it was awesome until I looked up and saw everyone in the classroom was bored. Talking later with other 4-year engineering students at a prestigious university, not only did no one think Julia Sets were fascinating, no one even knew what they were.
Well, most engineering students hate math so It's not really surprising. When I talk about how much I love math and talk about the extra maths technical electives that i'm planning on taking my engineering peers just ask me "why would you take extra math?".
2024 checking in! thanks for the surprise twist at the end lmao
The 1st 8 seconds of Numberphile's video on Graham's Number is hilariously good at giving an idea of it.
this is like the best tedx talk
Dat voice 5:43 - 5:52 ... Absolutely amazing
So tell me more about determinants in pascal's triangle. "Oh god yes! Day9 has prepared me for this moment! And Starcraft, but I'll save Starcraft for later."
this is the best video, im so glad you posted it
I really love math! I'm not that good at it but I think it's very beautiful. Two years ago I spend a whole year doing calculus (just lower classes because I never got it) and after really putting effort into it I got straight A's in all my writing and oral exams. I know that compared to the amount of math problems and ways it's not difficult but I never imagined that I would actually appreciate sitting down and differentiate equations before going to class.
"well whaddyou like??"
"I fuckin hate THAT!"
ROFLMAO xD
For a video about Graham's Number, it took you 6 whole minutes to start talking about it. Well done.
What? This is why am is beautiful! It's so fun to imagine things that can barely be imagined.
Fun fact: that 4 color theory was the first proof that used a computer to prove it. They came up with a number of graphs (as in dots with lines connecting them) and just fed it into the computer to brute force it. It was controversial when it came out (of course) but obviously once everyone warmed up to computers it was accepted (and retested I assume).
Ok, as a math guy myself, that e^2x joke is one of the funniest jokes I’ve ever heard
Wow! You're math folk. Pleasant surprise of the day.
I made a picture testing it out, and it worked easily. None of the same color touched. I used Red, blue, green and yellow. The middle was red, then the ones outside starting from Northwest (A), heading east in a circular pattern and ending up just south of A, went yellow, blue, green, yellow, blue, green.
I watched this live and just watched for like the 5th time to show my 7yo son who loves math and numbers
whoa i took discrete mathematics with this prof at ucsd. Most excellent professor ever.
THANK YOU DAY 9 I heard of a number so big you cant imagine it and couldnt find it but wanted to tell my friends about it and know it do not only know that it was Grahams Number but i can just show them your video!
day[9] is my hero
If you want some perspective, Vsauce does an episode on 52 factorial, and 52 factorial is about 3^7625597484935 times smaller than 3(Double Up Arrow)4 that he was talking about at 11:00