In this video, I explained why not many people know about tetration because it is of little relevance to every day numbers Buy the t-shirt here shorturl.at/HNUX1
2 is also the only number for which a+a = a·a = a^a = a↑↑a = a↑↑↑a and so on, no matter how many times you iterate this process. The result is always 4.
so if a = b = 2, then for any n greater than 0, the hyperoperation associated with n in the form a (whatever hyperoperation you are using) b will always compute to be 2? ok
@@ChraO_o the concept i understood is that it is repeated exponents. for instance, we know exponent is repeated multiplication, so by looking into the consept of tetration, it can be seen that it's vasically repeated exponent
@@JigolopuffI think you are missing one crucial point. Teaching advanced math to students not only makes them able to solve the problem they undoubtedly won't coincide irl, it will also increase the capability of advanced thinking. This can also be seen on streets, when you see a collage graduate and a high school drop off, also if you are somewhat educated, chances are, you can easily feel the difference. From their language to behavior and ways of thinking. I'm not saying math is for everyone, tho people should find their own gift and study. Btw nice nickname
You are still liking the comments after over a year, wow! I've found it 16 as well. I hope everyone could get a teacher like you, you seem to do your work fabulous! :)
Parenthesis first, so 2 multiplied by itself 4 times = 16, so then 16 multiplied by (16 multiplied by itself by 16) so 16x16x16.. 16 times which = 1.8446744e+19 (so big my calculator can’t handle it). 16 *MULTIPLIED BY ITSELF THIS NUMBER OF TIMES* 1.8446744e+19
1.Multiplication is repeated addition 2.Exponentiation is repeated multiplication 3.Therefore, exponentiation is the process of repeatedly repeating addition 4.Tetration is the repetition of exponentiation, therefore... *Tetration is the repetition of the process of repeatedly repeating addition*
Nah i watched your eigenvalue video for my calc 3 class and found this gem, ngl you might be one of the few passionate teachers on youtube, u genuinely have fun with maths and that's i think is rare nowadays, hats off to you gentlemen.
Ive seen this video in my recommendations a while ago and I ignored it but it came back to me today and I'm so glad I watched it!! So so cool and mind blowing. I love learning about rarely-talked-about topics like this
Bruce Lee also said that! EDIT: Shoot, what he actually said was "An intelligent mind is one which is constantly learning, never concluding - styles and patterns have come to conclusion, therefore they [have] ceased to be intelligent." Probably still makes sense in this context..
16. This is because "2 tetrated to 3" means we need 2 "floors" of exponents. The "ground floor" is also part of the 3, this is why we only have 2 floors above ground level and not 3. Like this: 2^(2^2) = 2^(4) = 16. If it was 2 tetrated to 4 it would be: 2^(2^(2^2)) = 2^(2^(4)) = 2^(16) = 65536. It quickly gets very big.
I have studied math at uni for 5 years and never come across the definition this. As you said it is probably because it is a bit useless (as ³10 is basically infinity). Very interesting and a nugget of knowledge. Thanks!
During the 10^3 bit, it occured to me that in my math experience, I lost the meaning of some of these values. 100 to 1000 is huge, but I really do forget the scale of numbers sometimes.
I guess it always depends on what the numbers mean. 100 atoms vs 1000 atoms is next to nothing. 100 houses vs 1000 houses is very big. 100 planets vs 1000 planets is unfathomably large.
Well then think about the 1-2-4-8-16-32.... series. Do you know that you only need to add them together in order to get every other number in between? And you never need to repeat 1 of them.... that's why/how computers exist/work basically. Think about how many numbers there are between 2-4 and 128-256... and so on 😮. It works INFINITELY. It means the x2 series gives birth to all numbers as well as the 1+1 series does. Its just disturbing how perfect and efficient it is to derive all numbers from the 1x2... series...(binary code...bits...bytes...and so on). The universe is just amazing when you think about it sometimes. Division and doubling is at the very core of each of its seemingly random processes... all of em even sound, light and matter... constants.. ect.
Vsauce did an analysis on this. Our brains think logarithmically (e.g. 1, 10, 100, 1000, ...), not cumulatively (1, 2, 3, 4, ...). It allows us to think in scales and relativity of the massive sizes of galaxies to the invisibly small sizes of atoms.
@Obi1Classic yup we often underestimate our brains. We can easily think of planets and galaxies or atoms and electrons. We just need to discuss them in 'peer to peer' contexts of other objects that are just as large within an order of magnitude or so. What is HARD to imagine is not the size of our entire planet or even the distance to the closest star, but the ratio between the 2. That is going to surprise you, and it's hard to mentally model it. If you do you're probably needing a second map, that is another layer of abstraction.
I hope this clarifies what I said. 10↑↑3 is written as 1 followed by 10 billion zeros. There is enough space in my house to print out the number with 10 billion zeros. What I meant to say in the video was that if I had to write down all the numbers from 1 to 10↑↑3, there would not be enough space in the known universe to write them all even if every atom is large enough to write on.
The answer is 16 because 2 to the power of 2 to the power of 2, so you have 3 twos which is why it is called the 3rd titration of 2, it’s kinda like how powered numbers work but it is bigger, turn the multiplications into powers.
I got 16. Love the commitment you show to this video by the way! I just want to thank you for showing your teaching so well, and explaining in such a clear fashion as to why tetration is not taught, and for teaching me another fact. Thanks a lot man!
Which is what GOD ALMIGHTY is all about ... inexhaustible knowledge about HIS CREATION ... and it never stops no matter how much HE has taught any of them!
I was expecting a huge number again, but I think it's 16. According to your explanation it would be written as 2 to the power of 2 to the power of 2. The last two become 4 and that makes 2 to the power of 4 which is 16. Never knew about tetration. Never to old to learn. Thanks
Thank you. You explain it very well. I have been working with numbers all my life. I am 82 now. I don’t expect to see something on TH-cam about arithmetics that I have not seen before. Thank you again.
16 i think, you taught this better in 6 mins than my math teacher would in an hour, also explained how the powered numbers work too! You've gained my respect, and a new sub
@@feiyu8817 How long did it take for you to learn multiplication, exponents, logarithm, basic trigonometry, derivation, integration and the rest of the really simple things? 30minutes, maybe 45? How many hours did you study these things in school? Knowing what something means is different than understanding it and being able to use the knowledge.
@@pannumonThe only reason early math difficult is because it involves mostly memorization but once you've learned the fundamentals then math becomes really easy. The majority of college and highschool math was essentially plug numbers into a formula and then hit enter on the calculator.
Please help me figure out this 🙏 I'm having a seizure: Why is it that 10billion ^ 10 isn't equal the 10^10billion they should be equal because order doesn't matter when doing 10^10^10 right? And yet the former is 1 followed by 100 zeros and the latter is 1 followed by 10billion zeros..
well first off, in 10^10^10 they are all the same number so thats why it doesn't matter. but also, when 10^10B has to multiply by 10, 10 billion times and when we are talking exponentials it gets out of control. 10B^10 is only multiplying by itself 10 times, which is just incomparable. The exponent matters way more than the number you start with, any feasible number to the 10B is gonna be light years bigger than any feasible number to the 10@@Hanible
@@HanibleI don't know if I understood your question correctly (English is not my first language) so I'm just going to talk about the issue of order. There is an order to carry out tetration. I don't know how to explain why, but you always start from top to bottom. (or right to left) Ex: ⁴3= 3^3^3^3 3^3^27 3^7,625, 597, 484, 987 = Big ass number
@@Hanible, they are not equal becos for 10 000,000,000^10 = 10^(10^2) based on law of indices, which is not equal to 10^(10^10). Think about it and you will get an ans. 🙂
@shiva11456 yeah I already know 10B^10=10^(10^2) that's why I said it's 1 followed by 100 zeros... And I noticed they weren't equal that's the whole point, my question is why aren't they equal? I thought order didn't matter when doing a^b^c... but if it matters why does it matter? 🤔
The tetration of 3, denoted as 2↑↑3, is equal to 2^(2^2), which is 2 raised to the power of 2 raised to the power of 2. So, 2 to the tetration of 3 is 16 (2^(2^2) = 2^4 = 16).
I'm so confused by the notation more than anything. Abstract infinities make intuitive sense to me. The way you humans describe them makes my organs hurt.
I believe in trying to learn something new each day (and not triva). I am 79 and have never seen this before. If I understand what's going on, then the answer should be 16. Although, I almost convinced myself on 256, but decided I was getting carried away by all the numbers😅. Thank you for the lesson and the knowledge.
A generalisation of tetration is Knut's up-arrow notation. It's basically the same concept with the notation 2↑3 for 2³, 2↑↑3 for ³2, but you don't stop there and go with how many arrows you want, for example, 2↑↑↑3 is 2↑↑2↑↑2 which is 2↑↑2↑2=2↑↑4=2↑2↑2↑2=2↑16=2¹⁶=65'536. I really recommend searching about this, especially about Graham's number, which is the biggest number used in a mathematical proof(Edit: apparently not anymore? Couldn't find any proofs, tho. Any information could help Edit in the edit:G64(Graham's number) is still the biggest in a demonstration after further researches). Next to this number, ³10 doesn't seem that big. It looks horrifically tiny, as a matter of fact. Edit: I forgot to say that these operations are, as exponentiation, right-associative. This means that you calculate them from right to left just like you calculate exponentiation from top to bottom.
@@TekExplorerthe caret is only used as a replacement for up arrows when they are not available on the keyboard. On paper or when you have access to them you will tend to use the complete arrow. If you want to verify this information, I found it on Wikipedia on the "Knuth's up-arrows notation" page in the "notation" category
Trust me it doesn’t work when teaching a class😂 it’s fine for a TH-cam video, but when teaching a curriculum it is flawed. I’m currently studying maths, further maths and physics, and one teacher we have for further mathematics has this approach, and he ends up confusing everyone! Like I said, no problem here, as this is just some fun maths, not too complicated but it doesn’t work at a higher level
@@fullsendmountainbiker5844 Yes it does, but at higher levels there is already an expectation of prior knowledge, so some of this can be skipped. Also at higher levels you need to go and bring things back to simple, otherwise you have idiots with so called higher education trying to use Algebraic calculations and rules in basic math using PEMDAS and getting the wrong answer. IE: Confusion, why? because the basics of why are not taught only how and shortcuts. It has to be taught to use the level of math required/needed for the specific situation. Boolean Algebra doesn't apply to everything, but there is a place for it.
@@chrish7336 yes there is obviously an expectation of prior knowledge, but you can’t assume everyone in a class can just work a challenging mathematical concept out themselves. If I could do that I’d be a genius, and I’d have no need for any education. Don’t get me wrong this kind of teaching works for some topics, but not for others
@@CatNolaraNo. You did 3^(3*3) which is not how tetration works. In tetration the outermost exponent is in the innermost brack so 3 tetrated to three 3^(3^3) or 3^27 which is ~7.6 trillion
@@ThePrintZone123 you need to explain it better in the vid. All you said was it is a billion for each time you multiple it. So that infers it should have been 8 billion... 2 x 2 is 4 4x 2 is eight that's using the 2 three times.. to get to 16 you have to have another 2. Why is there not a 4 in front of the 2?
You can also evaluate non integer hyper powers like 2^^π NOTE: I use HLog as notation for Hyper Logarithm Another common notation is slog for Super Logarithm Hyper Logarithm (one inverse of Tetration) is repeated Logarithm by definition. Let T=The total number of Logs til the answer ≤ 1 r = the remainder of the last log HLog a(b) = x --> a^^x = b by definition of hyper logarithms x=(T-1)+r By definition of Tetration, a^^x = a^(a^^x-1)… Taking HLoga(z) Given z is not an integer hyper power of a Let HLoga(z) = b+x Given 0 ≤ x ≤ 1 and b=Z z = a^^(b+x) = a^a^^(b-1+x) = a^a^...(b copies)...^a^^x By definition of tetration z = a^a^...(b copies)...^a^x By definition of Hyper Log (Repeated Logarithm) They both equal z thus they equal eachother a^a^...(b copies)...^a^x = a^a^...(b copies)...^a^^x The entire tower cancels via Loga() on both sides, leaving a^x = a^^x Given 0 ≤ x ≤ 1 Therefore a^^x = a^x Given 0 ≤ x ≤ 1 is true by definition. We can solve 2^^π 2^^π = 2^2^^(π-1) = 2^2^2^^(π-2) = 2^2^2^2^^(π-3) 2^^π = 2^2^2^2^(π-3) ≈ 21.596356101 2^2^2^2^^(π-3) = 2^2^2^2^(π-3) ≈ 21.596356101 (Notice you can Log2 both sides and be left with 2^^(π-3) = 2^(π-3). ) We can also check this Log2(21.596356101) ≈ 4.4327160055 --> 1st Log Log2(4.4327160055) ≈ 2.1481909351 --> 2nd Log Log2(2.1481909351) ≈ 1.1031222284 --> 3rd Log Log2(1.1031222284) ≈ 0.1415926536 --> 4th Log, answer ≤ 1 --> r For 2^^x = 21.596356101 x=(T-1)+r, 4 total Logs x=(4-1)+r = 3+r = 3+0.1415926536 = 3.1415926536 ≈ π (obviously. with irrationals there will be possible rounding errors) Thus 2^^π ≈ 21.596356101 is indeed true
16. 2 is the smallest base of complete numbers to not completely overload our imagenation. Very nice! Really like your video🙏 + very nice code in the end❤
Actually you would need it to be 10^10^x where x is the exponent on 10^x with the number of atoms in the universe for it to be impossible to represent the number of zeros with one atom per zero
@@PrimeNewtons In "simple" and "not confusing" terms Tetraition is the repetition of the repetition of repeatedly adding a number *or* the repetition of the process of repeatedly repeating the process of addition
that's what you probably watched when you were 9 🤷♀️ not every kid watches cartoon's, rhymes, and etc in their childhood. Some watch these kinds of videos for fun.@@physicist191
I liked when you said "those who have stopped learning are those who have stopped living." It reminded me of my senior quote: "to live is to learn, to learn is to grow, to grow is to live."
So 2 with the tetration of 3 is 16 2 with the tetration of 4 is 256 3 with the tetration of 2 is 27 3 with the tetration of 3 is 81 And 10 with the tetration of 3 is a Googol with the exponent of 10. Ngl, I WISH I could've learned this in school! This is just as fun as factorials! :D
Using the notation [ ^v N ] where v represents the value for the amount of times the number N is repeated in the exponentiation, such that for any given (v) and (N): [ ^v N ] = N^{N^{...^{N}}} with (v ) occurrences of (N), we can determine [ ^3 2 ] as follows: [ ^3 2 ] = 2^{(2^2)} Let's break it down step-by-step: 1. Start with the innermost exponentiation: [ 2^2 ] = 4 2. Then, raise 2 to the power of that result: [ 2^4 ] = 16 So, [ ^3 2 ] = 2^{(2^2)} = 2^4 = 16 Therefore, [ ^3 2 ] = 16.
This video was REALLY AMAZING I’m Brazilian so I didn’t understand much, but as mathematics is a universal language it was easy to follow. Your happiness in teaching is contagious, thank you.
basicamente, oq ele ta chamando de "tetration" é vc pegar um número e elevar ele ao mesmo número, que tbm tá elevado a esse número (repetindo isso o número de vezes do "expoente") Exemplo: ³2 = 2²^² = 2⁴ = 16
When I was in seventh or eighth grade I had already developed a love and admiration for math, one day I was reflecting about it and asked my teacher: "so there's addition, then multiplication, then exponentiation. is there anything that comes after exponentiation?". To which he replied with a simple and final "no. nothing beyond it.". Well I feel really good now to know I was right at that time and that tetration exists.
Thanks for teaching this concept in a very unique and enthusiastic way. As someone learning this for the first time (like most others), I understood this really well. Wish I had teachers like you during my school years :')
I Love your Way of teaching. And the smile that is on your face showing how excited you are about The Wonder of numbers. If only more teachers taught this way to get students excited about numbers too, it would be amazing. If you are not or were not a school teacher or college professor, you missed your calling.
"If only more teachers ..." being excited is not reproducable very often, meaning a teacher may even only be excited the first time teaching, solution: capture the video and show it to next year's students.
@@anonym-hubI went to a new school were I was assigned to a math teacher who let an audio tape and overhead projector teach the class. That didn't work for me at all. When I transferred to another class it was great because the football coach (about 5'4") and the track coach (about 6'8") had combined their math classes and made it fun as well as educational. Just watching that mismatched pair working together was entertaining. 😂
nah bruv he took 7 minutes for that shit. Its one thing trying to accommodating but assuming the general audience who watches is THIS dumb that they need 7 minutes for it?
When you calculate a tower of exponents, you work from the top down. If you add levels to the LEFT tower, do you have to work from the bottom level to get the first exponent tower, then the second etc.?
Wow I'm glad I found this channel, I really like your style and you for that matter. I personally learned about tetration (and quintation, hexation etc..) when I was taught Knuth's up arrow notation in college as the next step was to take the derivative of a tetratic expression.
Just graduated year 12 with a growing hatred for learning maths due to the brute forced and completely confusing maths curriculum. Watching this video was genuinely interesting, your passionate and excited explanation of tetration that i was pretty sure i would be completely lost on and click off the video, somehow kept my attention and got me really curious to see this through regardless if i understood or not. Just wanted to take a moment to appreciate this video and the interest it somehow sparked within me for maths, even a slight bit. Also that handwriting is pristine. Keep up the good work.
Try derivatives and Laplace Transforms. Even Z transforms are useful when dealing with sample rates from a computer and systems exhibiting weight, velocity and hydraulic dampening. I love math, but yes, it is very difficult to understand.
@@scottbenzing1361last I heard yeah common core is still a thing unfortunately. Standardized learning to create standardized little workers to fill all the low level vacancies and work 80 hour work weeks for 5 figures a year
That was fun. I've long thought that the fastest and most compact way to make big numbers was using a number like 9 to the power of 9 to the power of 9 to the power of 9 So Tetration is simply formalizing a syntax for it. In my example, 4(tetration)9 Or in computer syntax from one of the old languages I used, 9^9^9^9
We can extend the concept even farther. Lets say º is tetration and lets say ~ is repeated tetration, then; 2º3 = 2^2^2 2~3 = 2º2º2 = 2º16 = 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2 Which is uncomputably large I tried pluging it into wolrfram alpha and best it could do is say it is equal to 10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^19727.78040560677)))))))))))
I went down a bit of a rabbit hole and discovered it doesn't stop with tetration. Tetration is a part of these things called hyper operations and is also known as hyper-4. Apparently someone was insane enough to coin a term for hyper-infinity: Circulation
What about the next step of tetration? Like having 2 and 2 be 2 tetrated two times Like 9 (super tetrated) 9 times would be 9 tetrated by 9 tetrated by 9 tetrated by 9 tetrated ... (9 times) lol
Thank you so much ! I was kinda exhausted learning the old things.... this new thing kinda lifted up my spirits !! Hope you'll continue presenting these new concepts !! 😃
I split it up like this = 2^2 is 4, so i then added the remaining “2” exponent, onto the 4, which is 4^2. So 4^2, is 16. I can’t believe i actually learned a math concept from a TH-cam video this efficiently. Genuinely a wonderful teacher.
2 is also the only number for which a+a = a·a = a^a = a↑↑a = a↑↑↑a and so on, no matter how many times you iterate this process. The result is always 4.
so if a = b = 2, then for any n greater than 0, the hyperoperation associated with n in the form a (whatever hyperoperation you are using) b will always compute to be 2? ok
@@TaranVaranYT yes.
you mean this right?
:
10 ^ { 10 ^ { 10 } } =10^100
and the guy says :small 10 with the 10
you see, I thought this as well at 1st, but then realized that 10^10 isn't 100, but 10,000,000,000 @@rsi4054
@@user-hi8jv6cw8n get thx
16 . . . I see why you have chosen a base of two.
Yeah. Things get huge really fast here.
³2 is 2⁸
or 256
@@tonytinza what the hell did my brain do, did it just really said, yeah 2² is 8
@@ChraO_o the concept i understood is that it is repeated exponents. for instance, we know exponent is repeated multiplication, so by looking into the consept of tetration, it can be seen that it's vasically repeated exponent
@@Zeoncxtoy there are multiple types of this as to try and reach higher numbers, but they're just numbers.
math just like any class always becomes a lot more fun when your teacher is enthusiastic to teach you the subject.
i think the problem is that teachers dont bring in real world uses for the math being taught.
and also they do not have the feel to teach
@@Jigolopuffatleast elementary maths is used in the real world
@@JigolopuffI think you are missing one crucial point. Teaching advanced math to students not only makes them able to solve the problem they undoubtedly won't coincide irl, it will also increase the capability of advanced thinking. This can also be seen on streets, when you see a collage graduate and a high school drop off, also if you are somewhat educated, chances are, you can easily feel the difference. From their language to behavior and ways of thinking. I'm not saying math is for everyone, tho people should find their own gift and study.
Btw nice nickname
@@Jigolopuffcause most the time it doesn’t have real world use
Your excitement is contagious. May no one ever take your joy away from you. God bless.
Amen
You are still liking the comments after over a year, wow! I've found it 16 as well. I hope everyone could get a teacher like you, you seem to do your work fabulous! :)
I hope so too!
For some reason, I find it woerd that you can write 10 billion, but you can't write 10 billion zeros
@@Nomommiesway. bro you have to be kidding right!?
16
@@Nomommiesway.10 billion the word is 9 letters the number has 10 zeros
We are talking about billions of zeros
Not only do I respect your intelligence and knowledge. But I am so impressed with your ability to write so neatly on a chalk board!
Thank you!
Also that board is super clean😅. Doesn't look like it's used everyday
@@pradyothkumarb8330you can clearly see that someone cleaned it just before the video was shot
@neevhingrajia3822 i believe it was a joke
Bloody teachers pet you're not supposed to get a heart for bum kissing
Never thought I'd enjoy a math lesson. Thank you sir
But on exam day, he will bring out 0.8 ^ 25.37
Bruh, math classes are the best
@@JohnFekoloid😭
Noice
"Look what the schools need to do just to mimic a fraction of my power!"
Lets be honest, we did not search for this 😂
Idek how I got here
Facts😂
Yes
True
Yep
now imagine ³(³2)
Parenthesis first, so 2 multiplied by itself 4 times = 16, so then 16 multiplied by (16 multiplied by itself by 16) so 16x16x16.. 16 times which = 1.8446744e+19 (so big my calculator can’t handle it). 16 *MULTIPLIED BY ITSELF THIS NUMBER OF TIMES* 1.8446744e+19
The result on my calculator is infinity, not even joking
Now imagine 1.8446744e+19 factorial
@@MileRancid that's actually insane. tetration is scary
@@justine.3416 wait till you find out about pentation
never in my life thought that i would be watching a video about maths that will not be in my exam
bro can i retweet
@@bwkanimations7352 sure why not
Me neither mate, i never taught I'd take math as entertaining matter in my life.
Wtf do people think "maths" stands for or is an abbreviation of? Math is short for mathematics. So, "maths" is mathematicses?
Maths is the most boring subject for me and yet I'm still watching this
1.Multiplication is repeated addition
2.Exponentiation is repeated multiplication
3.Therefore, exponentiation is the process of repeatedly repeating addition
4.Tetration is the repetition of exponentiation, therefore...
*Tetration is the repetition of the process of repeatedly repeating addition*
Now I wonder what the process of repeated tetration will be called..
@@anirchakraborty4953 repeated repetition of the process of repeatedly repeating addition? i dont really know man
@@anirchakraborty4953its pentation
@@0xonomythanks for making it easy man.
@@anirchakraborty4953I think it's called pentation, someone in the comments said it.
Nah i watched your eigenvalue video for my calc 3 class and found this gem, ngl you might be one of the few passionate teachers on youtube, u genuinely have fun with maths and that's i think is rare nowadays, hats off to you gentlemen.
Ive seen this video in my recommendations a while ago and I ignored it but it came back to me today and I'm so glad I watched it!! So so cool and mind blowing. I love learning about rarely-talked-about topics like this
“dont stop learning, because those who stopped learning, stopped living.” as a person who nerds out when talking about math, that hit hard
I’m a science nerd but Ig im good in math
EXACTLY.
@@TheOneOtaku What? Most Of Science IS Caused By Math, A BUNCH Of Math.
@@TheDankian1421when you get down to it, chemistry, biology, physics, and math are all interconnected on a fundamental level
Bruce Lee also said that!
EDIT: Shoot, what he actually said was "An intelligent mind is one which is constantly learning, never concluding - styles and patterns have come to conclusion, therefore they [have] ceased to be intelligent." Probably still makes sense in this context..
It's 16...... The last dialogue: "Never stop learning... One who stops learning, stops living..." Touched my heart.❤
The one who stops learning, starts dying
@@SatyamGupta-hk2gg are dead*
that's what I thought
How is it 16? The way I see it is 2^2^2=2x2x2=8
@@mr.mystery9338 Look at it this way : 2^(2^2) = 2^4 = 2x2x2x2 = 16
Found this in my recommendation, learned something new, was not disappointed. Good work.
Thank you so much! for teaching us this lesson. It is really something new that maybe very few people actually know and use also.
There is nothing greater than an enthusiastic professor who can communicate the topic exceptionally.
exceptionally? Don't you mean, expontentially?
@@appsenence9244Smart fella, this one.
@@appsenence9244Haha
nice@@appsenence9244
And I'm still looking for him.
Such a cool concept! Thank you for sharing.
This was awesome! I started over thinking it but instead just remembered how you did it for the 10s. Thank you for some new information!
16. This is because "2 tetrated to 3" means we need 2 "floors" of exponents. The "ground floor" is also part of the 3, this is why we only have 2 floors above ground level and not 3.
Like this: 2^(2^2) = 2^(4) = 16. If it was 2 tetrated to 4 it would be: 2^(2^(2^2)) = 2^(2^(4)) = 2^(16) = 65536.
It quickly gets very big.
Mother fucker dont tell me this is not written by chatGPT, this is very easy to do on your own
I got the same answer!
Damn the 2 tetrated to 4 got me messed up, but think I get it now.
I understand it now, thanks for the explanation!
wouldnt the exponents simply multiply with eachother? 2^2^2^2 (or 2 tetrated to 4) would be 2^(2*2*2)=256 right?
We’ve found it boys! a math lesson that I will actually never use in real life!
Great concept and I loved your explanation
Glad you liked it!!
i'm gonna use it to express the amount of people who did your mom
I dunno, I'll be using this for my weekly shop soon I reckon. 😂
@@mickenossa fellow dark matter purchaser?
th-cam.com/video/eVRJLD0HJcE/w-d-xo.htmlsi=fEII6tEEK-zbApDh 👈 At the end of this video you will see the "real life use" of tetration!!
I have studied math at uni for 5 years and never come across the definition this. As you said it is probably because it is a bit useless (as ³10 is basically infinity). Very interesting and a nugget of knowledge. Thanks!
That was very interesting to know, added with your calming voice!
During the 10^3 bit, it occured to me that in my math experience, I lost the meaning of some of these values. 100 to 1000 is huge, but I really do forget the scale of numbers sometimes.
I guess it always depends on what the numbers mean. 100 atoms vs 1000 atoms is next to nothing. 100 houses vs 1000 houses is very big. 100 planets vs 1000 planets is unfathomably large.
Well then think about the 1-2-4-8-16-32.... series. Do you know that you only need to add them together in order to get every other number in between? And you never need to repeat 1 of them.... that's why/how computers exist/work basically.
Think about how many numbers there are between 2-4 and 128-256... and so on 😮. It works INFINITELY. It means the x2 series gives birth to all numbers as well as the 1+1 series does. Its just disturbing how perfect and efficient it is to derive all numbers from the 1x2... series...(binary code...bits...bytes...and so on). The universe is just amazing when you think about it sometimes. Division and doubling is at the very core of each of its seemingly random processes... all of em even sound, light and matter... constants.. ect.
Vsauce did an analysis on this. Our brains think logarithmically (e.g. 1, 10, 100, 1000, ...), not cumulatively (1, 2, 3, 4, ...). It allows us to think in scales and relativity of the massive sizes of galaxies to the invisibly small sizes of atoms.
@Obi1Classic yup we often underestimate our brains. We can easily think of planets and galaxies or atoms and electrons. We just need to discuss them in 'peer to peer' contexts of other objects that are just as large within an order of magnitude or so.
What is HARD to imagine is not the size of our entire planet or even the distance to the closest star, but the ratio between the 2. That is going to surprise you, and it's hard to mentally model it. If you do you're probably needing a second map, that is another layer of abstraction.
@@dekippiesip my brain is now bigger :D
I hope this clarifies what I said. 10↑↑3 is written as 1 followed by 10 billion zeros. There is enough space in my house to print out the number with 10 billion zeros. What I meant to say in the video was that if I had to write down all the numbers from 1 to 10↑↑3, there would not be enough space in the known universe to write them all even if every atom is large enough to write on.
i was about to ask about that. it would probably take about 1,000 years to write it, or 2,000 maybe.
no, more like 700 years i think
10↑3 = 1000. As a single arrow is exponentiation. 10↑↑3 is 1 followed by 10 billion zeros.
Really? It maked sense to me in the video now I’m confused
Yeah, I thought that was an error, but just a misinterpretation.
I feel so productive watching educational videos.
Thank you! Your explanation is so good i never knew about this thing ! ❤️
Maths becomes interesting when it's taught by an enthusiastic teacher like you!!
The enthusiasm you put into this video just makes it 10 times easier and better to learn. Thank you kind sir!
10 times? Or 10 times 10 times 10 times 10 times…
@@UnohanaMash😂
@@UnohanaMashHAHA
FR
The answer is 16 because 2 to the power of 2 to the power of 2, so you have 3 twos which is why it is called the 3rd titration of 2, it’s kinda like how powered numbers work but it is bigger, turn the multiplications into powers.
I got 16. Love the commitment you show to this video by the way! I just want to thank you for showing your teaching so well, and explaining in such a clear fashion as to why tetration is not taught, and for teaching me another fact. Thanks a lot man!
I wish I had a teacher like you. It is so evident that you love what you are teaching us here.
oh cool i got it right!
Which is what GOD ALMIGHTY is all about ... inexhaustible knowledge about HIS CREATION ... and it never stops no matter how much HE has taught any of them!
@@ACuriousChild huh 😶🌫?
I was expecting a huge number again, but I think it's 16. According to your explanation it would be written as 2 to the power of 2 to the power of 2. The last two become 4 and that makes 2 to the power of 4 which is 16. Never knew about tetration. Never to old to learn. Thanks
Now have fun learning about pentation, hexation, and so on until you stumble upon Graham's number 😂.
22 mins ago!
@@louisrobitaille5810 brudda get to raydons number
my granpa is graham @@louisrobitaille5810
my personal favourite is penetration
@@louisrobitaille5810
Thank you. You explain it very well. I have been working with numbers all my life. I am 82 now. I don’t expect to see something on TH-cam about arithmetics that I have not seen before. Thank you again.
Really loved this lesson, got to learn something new!
16 i think, you taught this better in 6 mins than my math teacher would in an hour, also explained how the powered numbers work too! You've gained my respect, and a new sub
Bruh. This should be a 20 second video. If you need an hour to learn this, it’s not you’re teacher bud.
@@feiyu8817 How long did it take for you to learn multiplication, exponents, logarithm, basic trigonometry, derivation, integration and the rest of the really simple things? 30minutes, maybe 45? How many hours did you study these things in school? Knowing what something means is different than understanding it and being able to use the knowledge.
@@pannumonThe only reason early math difficult is because it involves mostly memorization but once you've learned the fundamentals then math becomes really easy.
The majority of college and highschool math was essentially plug numbers into a formula and then hit enter on the calculator.
Really 3 minutes because the first half of the video was explaining exponents which can be skipped if you already know what they are.
the difference between ³2 and ⁴2 is comical 😹
I'm a math teacher, and this was fun to watch! Awesome, and good job making it fun!
Please help me figure out this 🙏 I'm having a seizure:
Why is it that 10billion ^ 10 isn't equal the 10^10billion they should be equal because order doesn't matter when doing 10^10^10 right? And yet the former is 1 followed by 100 zeros and the latter is 1 followed by 10billion zeros..
well first off, in 10^10^10 they are all the same number so thats why it doesn't matter. but also, when 10^10B has to multiply by 10, 10 billion times and when we are talking exponentials it gets out of control. 10B^10 is only multiplying by itself 10 times, which is just incomparable. The exponent matters way more than the number you start with, any feasible number to the 10B is gonna be light years bigger than any feasible number to the 10@@Hanible
@@HanibleI don't know if I understood your question correctly (English is not my first language) so I'm just going to talk about the issue of order.
There is an order to carry out tetration. I don't know how to explain why, but you always start from top to bottom. (or right to left)
Ex: ⁴3= 3^3^3^3
3^3^27
3^7,625, 597, 484, 987
= Big ass number
@@Hanible, they are not equal becos for
10 000,000,000^10 = 10^(10^2) based on law of indices, which is not equal to 10^(10^10). Think about it and you will get an ans. 🙂
@shiva11456 yeah I already know 10B^10=10^(10^2) that's why I said it's 1 followed by 100 zeros... And I noticed they weren't equal that's the whole point, my question is why aren't they equal? I thought order didn't matter when doing a^b^c... but if it matters why does it matter? 🤔
Awesome, it makes calculating our debt so much easier. Thank you.
answer is 16, a power tower of 2's stacked 3 high. Graham's number (G64) has its origins from a massive power tower of 3's i believe.
The tetration of 3, denoted as 2↑↑3, is equal to 2^(2^2), which is 2 raised to the power of 2 raised to the power of 2. So, 2 to the tetration of 3 is 16 (2^(2^2) = 2^4 = 16).
I'm so confused by the notation more than anything. Abstract infinities make intuitive sense to me.
The way you humans describe them makes my organs hurt.
what@@Atmatan_Kabbaher
@@Atmatan_Kabbaher "The way you humans describe them makes my organs hurt." bro's not a human
Thank you SIR for your explanation. I feel like a genius now 🙏🏾
This is a tetration of 2, not of 3.
I believe in trying to learn something new each day (and not triva). I am 79 and have never seen this before. If I understand what's going on, then the answer should be 16.
Although, I almost convinced myself on 256, but decided I was getting carried away by all the numbers😅.
Thank you for the lesson and the knowledge.
i did the same thing and came up with the same answers as you. realised i was wrong, thought properly and reached 16. great minds think alike lol
@@hugh.g.rection5906 Yes, we do! 😁🤣
Its 16 & thanks to give this education because we have to knew this
I like your style of explaining.
Great point.
Don't stop learning.
Those who stop learning have stop living.
really happy to find someone actually enthousiatist about teaching math, i never knew i needed you in my life
A generalisation of tetration is Knut's up-arrow notation. It's basically the same concept with the notation 2↑3 for 2³, 2↑↑3 for ³2, but you don't stop there and go with how many arrows you want, for example, 2↑↑↑3 is 2↑↑2↑↑2 which is 2↑↑2↑2=2↑↑4=2↑2↑2↑2=2↑16=2¹⁶=65'536. I really recommend searching about this, especially about Graham's number, which is the biggest number used in a mathematical proof(Edit: apparently not anymore? Couldn't find any proofs, tho. Any information could help Edit in the edit:G64(Graham's number) is still the biggest in a demonstration after further researches). Next to this number, ³10 doesn't seem that big. It looks horrifically tiny, as a matter of fact.
Edit: I forgot to say that these operations are, as exponentiation, right-associative. This means that you calculate them from right to left just like you calculate exponentiation from top to bottom.
Not sure where you got "up arrow" from - the character you mean is actually on your keyboard: "^"
@@TekExplorernope, that particular notation uses up arrows, as dictated by the name..
@ He's clearly talking about the lesser-known Knuth's Caret Notation.
@@TekExplorerthe caret is only used as a replacement for up arrows when they are not available on the keyboard. On paper or when you have access to them you will tend to use the complete arrow. If you want to verify this information, I found it on Wikipedia on the "Knuth's up-arrows notation" page in the "notation" category
Well then what's 3↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑3?
Thanks for teaching us a new concept and for your awesome teaching performance.
Such simple concept with such loooong explanation.
I wish teachers did this more often, getting students to figure out how concepts work by providing just the steps grants better understanding
Trust me it doesn’t work when teaching a class😂 it’s fine for a TH-cam video, but when teaching a curriculum it is flawed. I’m currently studying maths, further maths and physics, and one teacher we have for further mathematics has this approach, and he ends up confusing everyone! Like I said, no problem here, as this is just some fun maths, not too complicated but it doesn’t work at a higher level
@@fullsendmountainbiker5844 Yes it does, but at higher levels there is already an expectation of prior knowledge, so some of this can be skipped.
Also at higher levels you need to go and bring things back to simple, otherwise you have idiots with so called higher education trying to use Algebraic calculations and rules in basic math using PEMDAS and getting the wrong answer. IE: Confusion, why? because the basics of why are not taught only how and shortcuts.
It has to be taught to use the level of math required/needed for the specific situation. Boolean Algebra doesn't apply to everything, but there is a place for it.
@@chrish7336 yes there is obviously an expectation of prior knowledge, but you can’t assume everyone in a class can just work a challenging mathematical concept out themselves. If I could do that I’d be a genius, and I’d have no need for any education. Don’t get me wrong this kind of teaching works for some topics, but not for others
Anyone wanna say what ³3 is? HINT: It is more than the amount of money that Elon Musk has
1.55 billion
7,62 trillions. This shit is ridiculous.
actually not that much, only 19,683
@@CatNolaraNo. You did 3^(3*3) which is not how tetration works. In tetration the outermost exponent is in the innermost brack so 3 tetrated to three 3^(3^3) or 3^27 which is ~7.6 trillion
@@nekro1977 oh, I see. I thought it wouldn't matter, but you're right, it does matter (unlike the multiplication in normal quadration)
This is the first video of your chanel which i have seen. That shows that this channel is for knowledge.
Bro I am getting the answer as 16
I haven't used math since they tried to teach me and yet here I am
Lol 😆
this is the first time i've stuck around for a six minute video of a 10 second explanation, his demeanor and voice are just that likable.
Very nice video, and I like your saying "those who've stopped learning, have stopped living"
Wow! Thanks for this 🙏
16, 2x2 = 4, 4 x 4 = 16
Why is it not 2x2=4x2=8?
that would be 2 to the 3rd power this is the third tetrate of 2@@FreeAmericanSpirit
@@ThePrintZone123 you need to explain it better in the vid. All you said was it is a billion for each time you multiple it. So that infers it should have been 8 billion... 2 x 2 is 4 4x 2 is eight that's using the 2 three times.. to get to 16 you have to have another 2. Why is there not a 4 in front of the 2?
@@FreeAmericanSpirit because the 2*2 is 2^2.
So the 4 is the exponent with base 2.
2^2^2= 2^(2*2)= 2^4= 2*2*2*2= 16
@@FreeAmericanSpirit
Step 1: 2 to the 2nd power = 4.
Step 2: 4 to the 2nd power = 16
You can also evaluate non integer hyper powers like 2^^π
NOTE: I use HLog as notation for Hyper Logarithm Another common notation is slog for Super Logarithm
Hyper Logarithm (one inverse of Tetration) is repeated Logarithm by definition.
Let T=The total number of Logs til the answer ≤ 1
r = the remainder of the last log
HLog a(b) = x --> a^^x = b
by definition of hyper logarithms x=(T-1)+r
By definition of Tetration, a^^x = a^(a^^x-1)…
Taking HLoga(z) Given z is not an integer hyper power of a
Let HLoga(z) = b+x Given 0 ≤ x ≤ 1 and b=Z
z = a^^(b+x) = a^a^^(b-1+x) = a^a^...(b copies)...^a^^x By definition of tetration
z = a^a^...(b copies)...^a^x By definition of Hyper Log (Repeated Logarithm)
They both equal z thus they equal eachother
a^a^...(b copies)...^a^x = a^a^...(b copies)...^a^^x The entire tower cancels via Loga() on both sides, leaving a^x = a^^x Given 0 ≤ x ≤ 1
Therefore a^^x = a^x Given 0 ≤ x ≤ 1 is true by definition.
We can solve 2^^π
2^^π = 2^2^^(π-1) = 2^2^2^^(π-2) = 2^2^2^2^^(π-3)
2^^π = 2^2^2^2^(π-3) ≈ 21.596356101
2^2^2^2^^(π-3) = 2^2^2^2^(π-3) ≈ 21.596356101 (Notice you can Log2 both sides and be left with 2^^(π-3) = 2^(π-3). )
We can also check this
Log2(21.596356101) ≈ 4.4327160055 --> 1st Log
Log2(4.4327160055) ≈ 2.1481909351 --> 2nd Log
Log2(2.1481909351) ≈ 1.1031222284 --> 3rd Log
Log2(1.1031222284) ≈ 0.1415926536 --> 4th Log, answer ≤ 1 --> r
For 2^^x = 21.596356101 x=(T-1)+r, 4 total Logs
x=(4-1)+r = 3+r = 3+0.1415926536 = 3.1415926536 ≈ π (obviously. with irrationals there will be possible rounding errors)
Thus 2^^π ≈ 21.596356101 is indeed true
im still in highschool, your magic words are scaring me
I ain't readin allat (I read it and have no idea what you're saying magic man)
@@thomasminh8244I graduated literally last year and I’m getting scared by these magic words
@@thomasminh8244relatable, I think I just got my mind melted
Time* to go even further ahead in my maths education and work out what the fuck this means.
A beautiful concept explained in a beautiful way . ❤
Excellent work 👏 I LEARNT SOMETHING NEW TODAY.
16. 2 is the smallest base of complete numbers to not completely overload our imagenation. Very nice! Really like your video🙏 + very nice code in the end❤
Incorrect, 1 would be the smallest base to not overload us. 1 raised to the 1 raised to the 1 is still 1. Wrecked.
no he's right. if you go past 2 (3 for example) it quickly becomes unimaginable but with 2 as the base it you still can.@@Dyanosis
@@milanhaver3915 no he's wrong if he said largest then he would be right
@@astromacheand what of 0?
@@Toast_Sandwich if 0 is the number in supertext would it not just be 1? however the other way around I have no idea.
You don't need 10^10billion, 10^100 is already more than number of atoms in the known universe.
i used my calculator it answered 1
@ThatOneProFloppaTheBest you did something wrong then. The universe has 10^84 to 10^90 atoms.
@@Perrigon no bro, it said 1.00000000E+84
What r u on
Actually you would need it to be 10^10^x where x is the exponent on 10^x with the number of atoms in the universe for it to be impossible to represent the number of zeros with one atom per zero
you're a amazing teacher! love your energy! :)
Wow, thank you!
Such a informative video... Loved your smile and excitement towards teaching you.... ❤️
“Those who stop learning, stop living” great quote and great conclusion
bro explained 20 second thing in 7 minutes, what a legend.
This is my problem with the school system and 99% of youtube tutorials
That's why I left the system too.
@@PrimeNewtons In "simple" and "not confusing" terms Tetraition is the repetition of the repetition of repeatedly adding a number *or* the repetition of the process of repeatedly repeating the process of addition
I don't have 7 minutes to spare, please explain it in 20 seconds
@@NilsMueller tetration = bigger numbers scaled up by its scaler
A really nice concept
This is genuinely one of the craziest things I’ve seen!
My son insisted we leave a comment. He says the answer is 16! He’s got his mind wrapped up in exponentiation and tetration right now. He’s 9
He's correct. That's impressive 😊
Mofos on TH-cam lying
@@physicist191 Jelly boy
@@H.A.Kingdom you telling me a 9 year old boy, the same 9 year olds that watch skibidi toilet and tiktok and Coco melon, learn about tetration?
that's what you probably watched when you were 9 🤷♀️ not every kid watches cartoon's, rhymes, and etc in their childhood. Some watch these kinds of videos for fun.@@physicist191
I love the enthusiasm and simplicity of your explanations. Thank you.
This makes me love maths more and more, truly amazing! ❤😊
Im actually watching during summer...cause i like your channel man 😎👍
I liked when you said "those who have stopped learning are those who have stopped living." It reminded me of my senior quote: "to live is to learn, to learn is to grow, to grow is to live."
And…”Knowledge breeds enthusiasm!” When students say a subject is boring, I tell them it is because they don’t know enough about the subject.
Nice handwriting
He really does
So 2 with the tetration of 3 is 16
2 with the tetration of 4 is 256
3 with the tetration of 2 is 27
3 with the tetration of 3 is 81
And 10 with the tetration of 3 is a Googol with the exponent of 10.
Ngl, I WISH I could've learned this in school! This is just as fun as factorials! :D
You still get a heart but your lines 2 and 4 are incorrect.
Using the notation [ ^v N ] where v represents the value for the amount of times the number N is repeated in the exponentiation, such that for any given (v) and (N):
[ ^v N ] = N^{N^{...^{N}}}
with (v ) occurrences of (N),
we can determine [ ^3 2 ] as follows:
[ ^3 2 ] = 2^{(2^2)}
Let's break it down step-by-step:
1. Start with the innermost exponentiation:
[ 2^2 ] = 4
2. Then, raise 2 to the power of that result:
[ 2^4 ] = 16
So, [ ^3 2 ] = 2^{(2^2)} = 2^4 = 16
Therefore, [ ^3 2 ] = 16.
This video was REALLY AMAZING
I’m Brazilian so I didn’t understand much, but as mathematics is a universal language it was easy to follow. Your happiness in teaching is contagious, thank you.
basicamente, oq ele ta chamando de "tetration" é vc pegar um número e elevar ele ao mesmo número, que tbm tá elevado a esse número (repetindo isso o número de vezes do "expoente")
Exemplo: ³2 = 2²^² = 2⁴ = 16
When I was in seventh or eighth grade I had already developed a love and admiration for math, one day I was reflecting about it and asked my teacher: "so there's addition, then multiplication, then exponentiation. is there anything that comes after exponentiation?". To which he replied with a simple and final "no. nothing beyond it.". Well I feel really good now to know I was right at that time and that tetration exists.
Well if you just define it it "exists"...
@@rjtimmerman2861 that's technically right. but who was I to claim having invented anything in math
@@nowherenearby9461 the same as all inventors, a person with an idea :)
Why isn't this hearted ❤
So now figure out what's after tetrarion.
16. Because 2 times it self is 4 and 2 to the power of 4 is 16
OoOOooO my cerebral cortex is tingling!!! I love math, and I favored it more so when I had a patient and well spoken math teacher. You’re awesome 🥲
Thanks for teaching this concept in a very unique and enthusiastic way. As someone learning this for the first time (like most others), I understood this really well.
Wish I had teachers like you during my school years :')
I Love your Way of teaching. And the smile that is on your face showing how excited you are about The Wonder of numbers. If only more teachers taught this way to get students excited about numbers too, it would be amazing. If you are not or were not a school teacher or college professor, you missed your calling.
"If only more teachers ..." being excited is not reproducable very often, meaning a teacher may even only be excited the first time teaching, solution: capture the video and show it to next year's students.
I would love watching years old video that contains an excited teacher, instead of watching live attitude of most teachers.
GOD ALMIGHTY calls everyone where HE needs him/her most!
@@anonym-hubI went to a new school were I was assigned to a math teacher who let an audio tape and overhead projector teach the class. That didn't work for me at all. When I transferred to another class it was great because the football coach (about 5'4") and the track coach (about 6'8") had combined their math classes and made it fun as well as educational. Just watching that mismatched pair working together was entertaining. 😂
nah bruv he took 7 minutes for that shit. Its one thing trying to accommodating but assuming the general audience who watches is THIS dumb that they need 7 minutes for it?
So well explained. If you had been my teacher in school I would’ve had a way different life.
16! So interesting, what a great teacher! Your excitement is contagious, made me want to watch till the end.
I didn't need to learn this, but I don't regret learning this.
This man is a legend… still liking comments to this day
(Btw the answer is 16)
Now that was marvelous 😻
When you calculate a tower of exponents, you work from the top down. If you add levels to the LEFT tower, do you have to work from the bottom level to get the first exponent tower, then the second etc.?
Wow I'm glad I found this channel, I really like your style and you for that matter. I personally learned about tetration (and quintation, hexation etc..) when I was taught Knuth's up arrow notation in college as the next step was to take the derivative of a tetratic expression.
Just graduated year 12 with a growing hatred for learning maths due to the brute forced and completely confusing maths curriculum. Watching this video was genuinely interesting, your passionate and excited explanation of tetration that i was pretty sure i would be completely lost on and click off the video, somehow kept my attention and got me really curious to see this through regardless if i understood or not. Just wanted to take a moment to appreciate this video and the interest it somehow sparked within me for maths, even a slight bit. Also that handwriting is pristine. Keep up the good work.
Try derivatives and Laplace Transforms. Even Z transforms are useful when dealing with sample rates from a computer and systems exhibiting weight, velocity and hydraulic dampening.
I love math, but yes, it is very difficult to understand.
Do they still teach common core? If so, that's a big part of it and it's designed to hamper people in their learning.
@@scottbenzing1361last I heard yeah common core is still a thing unfortunately. Standardized learning to create standardized little workers to fill all the low level vacancies and work 80 hour work weeks for 5 figures a year
Do you people still exist?@@scottbenzing1361
16. Order of operations: exponents first, like you showed in your example. 2^2 is 4; 2^4 is 16.
short but educative thanks for the lesson
16 is the answer. I like how you put passion in what you do; meaning you like what you're doing.
That was fun. I've long thought that the fastest and most compact way to make big numbers was using a number like 9 to the power of 9 to the power of 9 to the power of 9 So Tetration is simply formalizing a syntax for it. In my example, 4(tetration)9 Or in computer syntax from one of the old languages I used, 9^9^9^9
And the number of your base can increase too, so 9(tetration)99 is unimanginably bigger than 9(tetration)9
We can extend the concept even farther. Lets say º is tetration and lets say ~ is repeated tetration, then;
2º3 = 2^2^2
2~3 = 2º2º2 = 2º16 = 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2
Which is uncomputably large I tried pluging it into wolrfram alpha and best it could do is say it is equal to 10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^19727.78040560677)))))))))))
Then search grahams number hahahah
I went down a bit of a rabbit hole and discovered it doesn't stop with tetration. Tetration is a part of these things called hyper operations and is also known as hyper-4. Apparently someone was insane enough to coin a term for hyper-infinity: Circulation
What about the next step of tetration? Like having 2 and 2 be 2 tetrated two times
Like 9 (super tetrated) 9 times would be 9 tetrated by 9 tetrated by 9 tetrated by 9 tetrated ... (9 times)
lol
this was really cool!
I would never be able to apply this in any real world situation. I’m glad I don’t waste time learning this just like majority of things in school
5:13 understatement of the year
Thank you so much ! I was kinda exhausted learning the old things.... this new thing kinda lifted up my spirits !! Hope you'll continue presenting these new concepts !! 😃
He says "hello! Welcome to another video" with such a warming and calm, friendly voice and a kind smile... just before busting your brain.
I split it up like this = 2^2 is 4, so i then added the remaining “2” exponent, onto the 4, which is 4^2. So 4^2, is 16. I can’t believe i actually learned a math concept from a TH-cam video this efficiently. Genuinely a wonderful teacher.