Why you didn't learn tetration in school[Tetration]

[@QUBIQUBED]

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*

[@abc4953xyz]

Now I wonder what the process of repeated tetration will be called..

[@0xonomy]

@@abc4953xyz repeated repetition of the process of repeatedly repeating addition? i dont really know man

[@MugsyBogues]

@@abc4953xyzits pentation

[@parthpatel9602]

​@@0xonomythanks for making it easy man.

[@TheNaz_O5-15]

​@@abc4953xyzI think it's called pentation, someone in the comments said it.

[@matthewstoicism1485]

16 . . . I see why you have chosen a base of two.

[@PrimeNewtons]

Yeah. Things get huge really fast here.

[@ChraO_o]

³2 is 2⁸ or 256

[@ChraO_o]

@@tonytinza what the hell did my brain do, did it just really said, yeah 2² is 8

[@Zeoncxtoy]

@@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

[@ChraO_o]

@@Zeoncxtoy there are multiple types of this as to try and reach higher numbers, but they're just numbers.

[@GnrMilligan]

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!

[@PrimeNewtons]

Thank you!

[@pradyothkumarb8330]

Also that board is super clean😅. Doesn't look like it's used everyday

[@neevhingrajia3822]

​​@@pradyothkumarb8330you can clearly see that someone cleaned it just before the video was shot

[@Everyoneneedsafriend]

​@neevhingrajia3822 i believe it was a joke

[@icantcook9998]

Bloody teachers pet you're not supposed to get a heart for bum kissing

[@adriantcullysover4640]

I like how excited and mind-blown he himself is before revealing the explanation. Thank you for this knowledge, Chief!

[@NoNameX_X0]

math just like any class always becomes a lot more fun when your teacher is enthusiastic to teach you the subject.

[@Jigolopuff]

i think the problem is that teachers dont bring in real world uses for the math being taught.

[@satswak]

and also they do not have the feel to teach

[@fenidiv4325]

​@@Jigolopuffatleast elementary maths is used in the real world

[@Alwaysright42250]

​​@@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

[@jaimelannister1797]

@@Jigolopuffcause most the time it doesn’t have real world use

[@pranavvishwekar2509]

It's 16...... The last dialogue: "Never stop learning... One who stops learning, stops living..." Touched my heart.❤

[@SatyamGupta-hk2gg]

The one who stops learning, starts dying

[@WeeMasterEmerald]

@@SatyamGupta-hk2gg are dead*

[@RedSkeletone]

that's what I thought

[@mr.mystery9338]

How is it 16? The way I see it is 2^2^2=2x2x2=8

[@fredericlaviolette5041]

@@mr.mystery9338 Look at it this way : 2^(2^2) = 2^4 = 2x2x2x2 = 16

[@gongometube]

There is nothing greater than an enthusiastic professor who can communicate the topic exceptionally.

[@appsenence9244]

exceptionally? Don't you mean, expontentially?

[@peterproductions5015]

@@appsenence9244Smart fella, this one.

[@Quvexe]

​@@appsenence9244Haha

[@ethaniscool315]

nice@@appsenence9244

[@scottwatts3879]

And I'm still looking for him.

[@PickleJuic1379]

The answer is 16. Multiplication is repeated addition, & exponents are repeated multiplication, so as I suspected, tetration is repeated exponents. Just like how we would break 2 x 3 into 2+2+2, and 2 to the power of 3 into 2 x 2 x 2, we can break tetration into multiple parts. 2 to the power of 2 to the power of 2 is still awfully confusing, so let’s take it one step at a time. 2 to the power of 2 is 4. After solving the first 2 numbers, we are left with 4 squared (or 4 to the power of 2), which is 16. Hope this helps!

[@greenberrygk]

And pentation is repeated tetration etc

[@kwahlman]

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.

[@jirisebesta1497]

Mother fucker dont tell me this is not written by chatGPT, this is very easy to do on your own

[@nix_]

I got the same answer!

[@McSmurfy]

Damn the 2 tetrated to 4 got me messed up, but think I get it now.

[@SeeltheProgrammer]

I understand it now, thanks for the explanation!

[@voltznake9248]

wouldnt the exponents simply multiply with eachother? 2^2^2^2 (or 2 tetrated to 4) would be 2^(2*2*2)=256 right?

[@frtzkng]

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. To clarify, with "no matter how many times you iterate" I do not mean "no matter how many times you chain the term _a_ together". I mean it will always be 4 no matter how many arrows you add between two instances of a, if and only if a = 2.

[@TaranVaranYT]

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

[@blackovich]

@@TaranVaranYT yes.

[@rsi4054]

you mean this right? : 10 ^ { 10 ^ { 10 } } =10^100 and the guy says :small 10 with the 10

[@2045-z6o]

you see, I thought this as well at 1st, but then realized that 10^10 isn't 100, but 10,000,000,000 @@rsi4054

[@rsi4054]

@@2045-z6o get thx

[@wendigo7021]

never in my life thought that i would be watching a video about maths that will not be in my exam

[@bwkanimations7352]

bro can i retweet

[@wendigo7021]

@@bwkanimations7352 sure why not

[@BickBull]

Me neither mate, i never taught I'd take math as entertaining matter in my life.

[@Batmann_]

Wtf do people think "maths" stands for or is an abbreviation of? Math is short for mathematics. So, "maths" is mathematicses?

[@sabretoothc2591]

Maths is the most boring subject for me and yet I'm still watching this

[@jelz_49]

The answer is 16. Thank you 🙏🏼 Good teaching skills God blessed you 👍🏼

[@deltakyy3894]

“dont stop learning, because those who stopped learning, stopped living.” as a person who nerds out when talking about math, that hit hard

[@BlackMambaR1P]

I’m a science nerd but Ig im good in math

[@TheDankian1421]

EXACTLY.

[@TheDankian1421]

@@BlackMambaR1P What? Most Of Science IS Caused By Math, A BUNCH Of Math.

[@louiesatterwhite3885]

​@@TheDankian1421when you get down to it, chemistry, biology, physics, and math are all interconnected on a fundamental level

[@neth7826]

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..

[@krokeman]

We aren't taught that, because government does not want us to be able to calculate the national debt.

[@Aspru]

fire ahh comment

[@priyadarshinibvk]

Good one 👍

[@lukastace3154]

I'm crying 😭

[@bebophippie1781]

or the size of my junk.

[@nervestormv]

😂😂😂

[@paulyvii]

Never thought I'd enjoy a math lesson. Thank you sir

[@JohnFekoloid]

But on exam day, he will bring out 0.8 ^ 25.37

[@Gadottinho]

Bruh, math classes are the best

[@David280GG]

​@@JohnFekoloid😭

[@aprilbrandon3441]

Noice

[@mrkoyunreis]

"Look what the schools need to do just to mimic a fraction of my power!"

[@iamtnothefam23]

It would be 16 as the exponent of the exponent would multiply the exponent itself 2 times. (2*2=4). And after that, the base (2) can now be multiplied 4 times as the product of the exponents have already been given (4). So now, 2^4 should equal 16 since 2*2=4 and 2*2*2*2 can be broken down into 4*4 or 4^2 which would give us our answer of 16.

[@anointedone1995]

Your excitement is contagious. May no one ever take your joy away from you. God bless.

[@PrimeNewtons]

Amen

[@EricaLavors]

Contagious and infectious *32889😊❤

[@WIZARDGaming_2011]

Bro Jay Shree Ram too not only amen ❤​@@PrimeNewtons

[@pierrotzzz]

​@@WIZARDGaming_2011What?

[@WIZARDGaming_2011]

@@pierrotzzz it's our slogan of our religion Hinduism

[@simplyy.aviation]

Maths becomes interesting when it's taught by an enthusiastic teacher like you!!

[@IRHrok]

We’ve found it boys! a math lesson that I will actually never use in real life! Great concept and I loved your explanation

[@PrimeNewtons]

Glad you liked it!!

[@BerylliumBronze]

i'm gonna use it to express the amount of people who did your mom

[@mickenoss]

I dunno, I'll be using this for my weekly shop soon I reckon. 😂

[@Deathwindgames]

⁠@@mickenossa fellow dark matter purchaser?

[@Kaka_Doctor_91]

kzbin.info/www/bejne/m4e1e396Za19macsi=fEII6tEEK-zbApDh 👈 At the end of this video you will see the "real life use" of tetration!!

[@sairajgaitonde2260]

³2=2²^² (2 to the power of 2 to the power of 2) (2²)=2x2=4 (4)²=4×4=16 Thus, ³2=16 Thank you for this. It's a good exercise to regain my attention span.

[@EZLawUSA-TR]

Let’s keep the Graham’s number a secret to not spoil the moment for the OP! 😊

[@BradenBest]

That's incorrect. It happens to be the case that 2^4 and 4^2 are both 16, but you have to resolve the exponent first. If you try your methodology with the 10^^3 example, you'll get a measly 10^100 instead of the correct answer of 10^10000000000. All orders of hyperoperation from exponentiation up are explicitly right-associative. Technically, all binary math operations (operations with two operands) are right-associative, but the fact that addition and multiplication are commutative means you can do them in either order, and we read left-to-right in English so people like to take shortcuts. So when you see a "power tower" like a^b^c^...^z, the only correct interpretation is to start with y^z and work downwards, a^(b^(c^...^(y^z))...). Hyperoperations go further than tetration, so it's important to get the order right if you're going to work with them. For example, consider 3^^3. That's 3^(3^3), or 7.6 trillion (if you do it in the wrong order you'll only get 17576). These numbers grow EXTREMELY quickly--even 3^^5 (3^(3^(3^(3^3)))) utterly dwarfs a googolplex (a famous large number). If you recurse once more, you'll have pentation, 3^^^3, or 3^^(3^^3), or a "power tower" of 3's that is 7.6 trillion 3's tall. 3^^^3 is an absolute _monster_ of a number, but it doesn't stop there. Go up another layer and you have 3^^^^3, which is 3^^^(3^^^3), or a tetration chain whose length IS that 7.6 trillion item tall power tower of 3's--whatever the value of number that is (it's big, we're so far beyond "you couldn't write it down even if you put a 100 billion digits on grains of sand and filled the entire observable universe with them" at this point--these numbers are so big they can't even be imagined), that ridiculous number is how many times you're _tetrating_ 3 with itself, just to get an even more ridiculous number, 3^^^^3, which serves as the base or "layer 1" of Graham's number, or "g1". g2 is two 3's with _g1 arrows_ between them. Yes, that's right, going up just one level of recursion with these operations results in absolutely out of control growth, and you are suddenly faced with going up a number of levels of recursions that can barely even be comprehended. Any ability to even remotely imagine the scale of this is absolutely shattered by this point. g3 is two 3's with g2 arrows between them. Keep repeating this process and you'll reach Graham's number at g64. In case you don't appreciate just how quickly these things scale: 3 + 3 = 6 3 x 3 = 9 3 ^ 3 = 27 3^^3 = 7625597484987 3^^5 = 3^(3^7625597484987) 3^^^3 = 3^^7625597484987 It's worth stressing how much 3^^5 utterly _dwarfs_ a googolplex. Googolplex is 10^10^10^2, or 10^10^100. It's number with 10^100 digits. The number is so large that writing it down in all its glory is impossible and even if every human who is alive and has ever lived was writing zeroes as fast as they could for their whole lives since the big bang until now, we wouldn't have written down even 1% of the number. It's ridiculously huge, and yet, 3^^5 is 10^10^10^12.5, or more than 10^10^1000000000000. It's a number with 6×10^3638334640023 digits. And the gap between 3^^^3 and 3^^5 is unimaginably larger than the gap between 3^^5 and a googolplex. Frankly, 3^^^3 is larger than googolplex^googolplex. Further reading: Hyperoperation, Ackermann Function, Graham's Number, Operator Associativity

[@bunnybeetle1304]

I wish I had a teacher like you. It is so evident that you love what you are teaching us here.

[@bunnybeetle1304]

oh cool i got it right!

[@ACuriousChild]

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!

[@Arel_Kursat]

The enthusiasm you put into this video just makes it 10 times easier and better to learn. Thank you kind sir!

[@UnohanaMash]

10 times? Or 10 times 10 times 10 times 10 times…

[@MoonDark-mq8ex]

​@@UnohanaMash😂

[@MantoHazra]

​@@UnohanaMashHAHA

[@loganeliott6590]

FR

[@welcometochiles6156]

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.

[@randomguyontheinternet5030]

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.

[@sk8pkl]

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.

[@Obi1Classic]

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.

[@dekippiesip]

​@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.

[@welcometochiles6156]

@@dekippiesip my brain is now bigger :D

[@AnaVerona_]

This is the ultimate ASMR experience... Ever! I'm experiencing learning and relaxation at once. You are amazing.

[@Dr.Gro.]

Lets be honest, we did not search for this 😂

[@YaneliRomero-w9u]

Idek how I got here

[@RomeoPickering]

Facts😂

[@isp9365]

Yes

[@oof545]

True

[@BettyGirma7]

Yep

[@PrimeNewtons]

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.

[@lubomirkubasdQw4w9WgXcQ]

i was about to ask about that. it would probably take about 1,000 years to write it, or 2,000 maybe.

[@lubomirkubasdQw4w9WgXcQ]

no, more like 700 years i think

[@magentamonster]

10↑3 = 1000. As a single arrow is exponentiation. 10↑↑3 is 1 followed by 10 billion zeros.

[@davidturizo2847]

Really? It maked sense to me in the video now I’m confused

[@OJB42]

Yeah, I thought that was an error, but just a misinterpretation.

[@YaBoiATEG]

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]

Bruh. This should be a 20 second video. If you need an hour to learn this, it’s not you’re teacher bud.

[@pannumon]

@@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.

[@petelee2477]

​​​​@@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.

[@petelee2477]

Really 3 minutes because the first half of the video was explaining exponents which can be skipped if you already know what they are.

[@maggyfrog]

the difference between ³2 and ⁴2 is comical 😹

[@flederflick]

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

[@louisrobitaille5810]

Now have fun learning about pentation, hexation, and so on until you stumble upon Graham's number 😂.

[@Wilson-AM]

22 mins ago!

[@howtobasic2.031]

@@louisrobitaille5810 brudda get to raydons number

[@bzibubabbzibubab420]

my granpa is graham @@louisrobitaille5810

[@Carl_with_a_k_]

my personal favourite is penetration @@louisrobitaille5810

[@uzgunucurtma]

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! :)

[@PrimeNewtons]

I hope so too!

[@Nomommiesway.]

For some reason, I find it woerd that you can write 10 billion, but you can't write 10 billion zeros

[@anakinmeh928]

@@Nomommiesway. bro you have to be kidding right!?

[@Conductewd]

16

[@o_o888]

@@Nomommiesway.10 billion the word is 9 letters the number has 10 zeros We are talking about billions of zeros

[@juniocarvalho9883]

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.

[@rafaesisimo_h]

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

[@DannyJohn-x7x]

4:20, everybody.

[@hansky_vlr]

damn bro I am high as f

[@priyabratasaha3895]

Appreciated

[@19_aman97]

​@@hansky_vlr same mann

[@futotheone]

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).

[@Atmatan]

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.

[@El.Primo0]

what@@Atmatan

[@satgurs]

@@Atmatan "The way you humans describe them makes my organs hurt." bro's not a human

[@sefutho]

Thank you SIR for your explanation. I feel like a genius now 🙏🏾

[@jasminerochas-oq8jw]

This is a tetration of 2, not of 3.

[@Scarfy101]

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.

[@SPY-ce8qf]

“Those who stop learning, stop living” great quote and great conclusion

[@Builder161]

Thank you for sharing this. I learned something new and I believe that we all should strive to expand our knowledge base. You never know when something learn may become useful to you.

[@first-namelast-name]

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.

[@TekExplorer]

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..

[@l3dcobra120]

@ He's clearly talking about the lesser-known Knuth's Caret Notation.

[@first-namelast-name]

​@@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

[@Iammonke-293]

Well then what's 3↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑3?

[@mickaelcoulon5604]

really happy to find someone actually enthousiatist about teaching math, i never knew i needed you in my life

[@scotty3114]

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.

[@Hugh.G.Rectionx]

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

[@scotty3114]

@@Hugh.G.Rectionx Yes, we do! 😁🤣

[@Sheema_67890]

I'm so glad I learned and actually understood this concept even though I hate maths. It feels nice to actually understand maths. Thankyou for posting this.

[@jalenanderson9706]

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."

[@jballenger9240]

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.

[@Rand0m.Dice.1]

16. First, we do 2^2, which is 4. Then, we do 2 to the power of that 4, which equals 16 I originally had the wrong method, so I edited it

[@Imjusticebro]

Your process is incorrect but correct results.

[@平-o2n]

No, tetration is right-to-left.

[@SIimyGoblin]

³2 = 2²^² = 2⁴ = 2×2×2×2 = 16

[@Shadozcreeping]

​@@SIimyGoblinthe third tetration of two is (2^2)^2 you got the right answer but your method (and top comment) was incorrect

[@SIimyGoblin]

@@Shadozcreeping whats incorrect about it

[@cmills14916]

I'm a math teacher, and this was fun to watch! Awesome, and good job making it fun!

[@Hanible]

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..

[@gammergames3322]

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

[@Henry.25]

​@@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

[@shiva11456]

​@@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. 🙂

[@Hanible]

@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? 🤔

[@Ragnar452]

I have never ever seen this before. And I finished computer science. That is crazy. Thanks. Also the answer is 16 meaning 2^2^2. Amazing. I learned something new today.

[@ObeyCamp]

Man, I SO wish I had math teachers like you in school. I always loved math but few of my teachers did. Not only do you clearly love the subject, which is transformative when it comes to teaching, but there's just something about the way that you teach that is inherently very engaging, completely independent of the math. I can't put my finger on it, but it's there.

[@ryanman0083]

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

[@thomasminh8244]

im still in highschool, your magic words are scaring me

[@TheDiamondPro44]

I ain't readin allat (I read it and have no idea what you're saying magic man)

[@VictorianSnailGod]

@@thomasminh8244I graduated literally last year and I’m getting scared by these magic words

[@knoghtt]

​@@thomasminh8244relatable, I think I just got my mind melted

[@2.4TrillionLocusts]

TLDR

[@bryceverleur2884]

I wish teachers did this more often, getting students to figure out how concepts work by providing just the steps grants better understanding

[@fullsendmountainbiker5844]

Trust me it doesn’t work when teaching a class😂 it’s fine for a KZbin 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

[@chrish7336]

@@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.

[@fullsendmountainbiker5844]

@@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

[@Khaled-kardashev]

I'm never expected to love mathematics! It depends on who teaches you. Thank you, sir. You earned a new sub! +

[@subup4116]

Never in my life did I think that I would scroll on youtube and actually watch a video where I would hear something, I have never heard in my life. Tysm for sharing!! It was lowkey bussin

[@MyOneFiftiethOfADollar]

I would expect a person like yourself to hear something everyday that you have never heard in your life.

[@subup4116]

@@MyOneFiftiethOfADollar And that's why you're single

[@ganyu_literally]

You ratioed him 🔥

[@jerichojoe307]

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.

[@anonym-hub]

"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-hub]

I would love watching years old video that contains an excited teacher, instead of watching live attitude of most teachers.

[@ACuriousChild]

GOD ALMIGHTY calls everyone where HE needs him/her most!

[@johnshaw6702]

​@@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. 😂

[@roshsurana]

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?

[@Longest-Word-In-English]

Tetration is a mathematical operation that involves repeatedly raising a number to the power of itself. This operation is an extension of exponentiation, which involves raising a number to a specified power. In tetration, the number is raised to the power of itself multiple times in a tower-like structure. Tetration can result in very large numbers, making it a fascinating concept in mathematics. Mathematicians use tetration to explore complex patterns and relationships within numbers.

[@xkyoshi11]

Brought to you by ChatGPT.

[@mafuyuskibidisigmarizz]

oh my god, I remember discovering your channel a year ago, specifically a month after this video was released, I went over some of your videos at the time, and I was really blown away. After I switched my channel, I forgot the name of your channel, yet I was still thinking about this video, I’m really happy this got recommended to me again! Btw, the answer is 16

[@DavidChristopherCasey]

I love the enthusiasm and simplicity of your explanations. Thank you.

[@AdonizedeckAckahBlayMiezah]

16 is the answer. I like how you put passion in what you do; meaning you like what you're doing.

[@fatnerd9985]

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.

[@pixels303at-odysee9]

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.

[@scottbenzing1361]

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.

[@mrfoobz5709]

@@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

[@richr6249]

Do you people still exist?@@scottbenzing1361

[@timothylego5675]

Just saw this on my fyp! It took me a bit to figure out but im getting it now. If im not wrong, the way it works is 2x2= 4, and then 4x4= 16. And basically you multiply the product by the product. Thanks!

[@raaviolli]

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.

[@rjtimmerman2861]

Well if you just define it it "exists"...

[@raaviolli]

@@rjtimmerman2861 that's technically right. but who was I to claim having invented anything in math

[@rjtimmerman2861]

@@raaviolli the same as all inventors, a person with an idea :)

[@trafficbyintent]

Why isn't this hearted ❤

[@SAJe_53]

So now figure out what's after tetrarion.

[@nickaos6626]

bro explained 20 second thing in 7 minutes, what a legend.

[@SomeCowguy]

This is my problem with the school system and 99% of youtube tutorials

[@PrimeNewtons]

That's why I left the system too.

[@QUBIQUBED]

@@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

[@NilsMueller]

I don't have 7 minutes to spare, please explain it in 20 seconds

[@SomeCowguy]

@@NilsMueller tetration = bigger numbers scaled up by its scaler

[@huz653]

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.

[@Yroc_Mahnud]

Just realized this with exponentials after the first two minutes of this video. For any exponential number, the value of any number one exponential less is the value of the original number minus 90%. So 10^5 would be 100,000 x .90 = 90,000. 100,000 - 90,000 = 10,000 being 10^4. 10,000 x .90 = 9000. 10,000 - 9,000 = 1000 = 10^3. It's super interesting, helpful and I thank you so much for this.

[@Yroc_Mahnud]

2^2 =4 2^4 = 16. ^3 3. 3^3 = 27 3^27=7.6255975e+12. Wow, this gets crazy real fast. lol. Ty for the video. After posting this I also found a video about an even bigger number, best way to type it that I can think of without booting me off the channel is v3 2. So basically the exponential number is in the bottom left. Once again, thank you for your video.

[@Yroc_Mahnud]

This was almost as bad as trying to figure out how much reality exists using (XYZ)P²C^4.

[@fluiditynz]

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

[@nichtrauchervor]

And the number of your base can increase too, so 9(tetration)99 is unimanginably bigger than 9(tetration)9

[@RebelKeithy]

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)))))))))))

[@joseluiscuervolopez-mora1814]

Then search grahams number hahahah

[@dylandillpickle568]

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

[@Ascyt]

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

[@uglubuglu]

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 :')

[@draco2333]

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❤

[@Dyanosis]

Incorrect, 1 would be the smallest base to not overload us. 1 raised to the 1 raised to the 1 is still 1. Wrecked.

[@milanhaver3915]

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

[@astromache]

@@milanhaver3915 no he's wrong if he said largest then he would be right

[@Toast_Sandwich]

@@astromacheand what of 0?

[@astromache]

@@Toast_Sandwich if 0 is the number in supertext would it not just be 1? however the other way around I have no idea.

[@RealmsSMPStudios]

Pentation: I’m about to end this man’s whole career Hexation: allow me to introduce myself. Haptation: Run Octation: *death’s whistle*

[@mrbenwong86]

You don't need 10^10billion, 10^100 is already more than number of atoms in the known universe.

[@ThatOneProFloppaTheBest]

i used my calculator it answered 1

[@Perrigon]

​@ThatOneProFloppaTheBest you did something wrong then. The universe has 10^84 to 10^90 atoms.

[@ThatOneProFloppaTheBest]

@@Perrigon no bro, it said 1.00000000E+84

[@ZenGodXGaming]

What r u on

[@Hycubo]

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

[@DevonBering]

Anyone wanna say what ³3 is? HINT: It is more than the amount of money that Elon Musk has

[@chimyshark]

1.55 billion

[@noobiesensei6281]

7,62 trillions. This shit is ridiculous.

[@CatNolara]

actually not that much, only 19,683

[@nekro1977]

@@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

[@CatNolara]

@@nekro1977 oh, I see. I thought it wouldn't matter, but you're right, it does matter (unlike the multiplication in normal quadration)

[@locien182]

Teachers who teach with passion or excitement help people grasp the subject. You talked clear and to the point in a way that wasn't condescending loved it subbing now

[@Fluitvis]

First math video I voluntarily watched, really fun how you explain it so well

[@randomshow9366]

Im studying for my ACT and came across this video. The quote at the end is one that I hope to remember till my time on earth expires. "Those who stop learning, have stopped living." Very powerful and inspirational. Also I love how you teach and your smile and enthusiasm on the topic is very interesting and this is coming from a "bad" student that absolutely cannot stand math.

[@tommcwilliams1072]

If you hate math, you might have been abused. Hint: math is a language, and you're clearly doing just fine with English.

[@shinigamidied4114]

Dang this was so interesting! I got 16 by following your example, from the other comments it looks about right. Please keep making these, you're awesome!

[@Lohikaarme1984]

YT recommended me your channel out of the blue, and i'm so glad it did! i'm promoting TA (Tetration Awareness XD) whenever and wherever i can, tho i fully realise it's not very practical operation. But it's important in its own merit, just to remind us to keep our minds open and always expect something more out of the vastness of mathematics. Keep up the good work man! :)

[@NaveedKakal]

Is this a widely accepted notation or is there something spicy like a minority trying to push it into acceptance

[@Lohikaarme1984]

​@@NaveedKakal no, i dont think it is. More commonly approved is something called Knuth's up-arrow notation, it's being used to write operations of exponentiation and beyond. Standard exponentiation (let's say 2 to the power of 3) would be written as 2↑3 (it is kinda similar to the 2^3 - i'm not sure if the root of both is the same, but they do look suspiciously similar). Tetration, and any other higher iteration for that matter, would just be written with more arrows in a row. So 2 tetrated by 3 would be written as 2↑↑3. Pentation as 2↑↑↑3 , hexation as 2↑↑↑↑3 and so on. Tho for tetration itself i'm a huge fun of a notation presented in this video, i mean it's just more elegant and instantaneously resambles something related to exponentiation. There are other interesting unorthodox notations out there, like inverted sqrt sign for logarithm, try googling "A radical new look for logarithms". It's just brilliant. I've also come across proposals for trigonometric functions that, instead of traditional sin, cos, and tan, use a representation of a right triangle with only the two sides relevant to the respective operation. So, tan would be written as a horizontal and a vertical line meeting at the right angle, sin as a skewed and vertical line, and cos as a skewed and horizontal line. :)

[@jamx02]

It's 16. You inspired my interest on proof theory and large number theory. I've been learning about transfinite growth in the fast growing hierarchy, and it gets pretty scary.

[@jordisimon1451]

2 is the a very special number, since it is the only number apart from 1 that always evaluates to 4 when elevated, tetrated, pentated, octated, icosated, hectated, and so on to itself.

[@Aglassofwater67]

Depends on the number of the tetration or pentation, etc. If it is 2 to the tetration, pentration, octasion, etc. of 2 then yeah it just becomes 2 squared, which is 4. If the tetration or pentation is higher however, the number quickly becomes absurdly large. 2 to the tetration of 3 is 16, 2 to the pentation of 3 meanwhile is a whopping 65536. And i'm not even gonna talk about octation.

[@alenbeckerd6769]

Now isolate it.. 😂😂😂

[@jordisimon1451]

@@Aglassofwater67 I know that, that's it is precisely why it is a fun fact

[@nishitsaini1865]

Who penetrates it

[@insquared1868]

Also 2 is both a composite and a prime number. Composite - we can divide it by 2 Prime - It can only be divided by itself and 1

[@spudhead169]

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.

[@StheSharknl]

Recovering from a burnout, worked in finance. Your vid’s are great to get back into things again! Loooove your positive energy, much respect from 🇳🇱 processor. You are a great teacher!

[@l3o584]

So the 3 stands for how many times you raise it right? So its 2^2^2. So take one at the time; 2^(2^2) 2^2=4 and 2^4=16 That means if just that 2 would have been a 3 it would be 3^3^3 3^3=27 3^27=7625597484987 or if just the 3 would have been a 4 it would be 2^2^2^2=2^(2^2^2) 2^2^2=2^(2^2) 2^2‎ = 4 2^4‎ = 16 2^16‎ = 65 536 I see It gets out off handedly big quickly using tetration. This was really cool to learn, thanks from sweden!

[@ChinmayNaik7]

Tetration! ³2 = 2↑↑3 (using Knuth's up-arrow notation) Tetration is a repeated exponentiation: ³2 = 2^(2^(2)) = 2^4 = 2 × 2 × 2 × 2 = 16 So, ³2 = 16. Tetration examples: - ²3 = 2^(2^3) = 2^8 = 256 - ⁴2 = 2^(2^(2^2)) = 2^16 = 65,536

[@RyanLewis-Johnson-wq6xs]

That’s correct except to 2 to the 3rd tetration=16 not 256 and 3 to the 2nd tetration=27

[@walksaselk40]

I haven't used math since they tried to teach me and yet here I am

[@PrimeNewtons]

Lol 😆

[@Ricky_B4]

2 raised to the power of 2 is 4 raised to the pwer of 2 is 16. I could listen to you speak on any subject for hours and you would have my full undivided attention. We need more people like you in all walks of life. Thank you for sharing.

[@Archnouff]

Be careful. Your calculus works with this case, but you actually compute exponentiation right to left. 2 to the power of 2 is 4, then 2 to the power 4 is 16. It works in your case because 2^4 = 4^2, but if you replace 2 by 3 for example, you obtain 3^3^3 which is 3^27, not 27^3.

[@Archnouff]

From wikipedia : "Under the definition as repeated exponentiation, na means a^a^...^a, where n copies of a are iterated via exponentiation, right-to-left, i.e. the application of exponentiation n − 1 times.

[@kevinkall8547]

16 is right answer, where's his HEART?

[@mimicreeplayz2441]

This man is a legend… still liking comments to this day (Btw the answer is 16)

[@joso5554]

Answer is 2^4=16. It would be interesting to explain what tetration is used for if at all. And how it can be defined for a non integer tetration exponent, say for example 0.5.

[@theefatima]

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

[@daveg659]

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

[@PrimeNewtons]

He's correct. That's impressive 😊

[@physicist191]

Mofos on KZbin lying

[@H.A.Kingdom]

​@@physicist191 Jelly boy

[@physicist191]

@@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?

[@Yurilikesm3l0ns]

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

[@ruparelvishesh7194]

³2 = 2^2^2 = 2^4 = 16. Thank you so much! I learnt something new today!

[@deboranoah6985]

I wish you were my math teacher I love how enthusiasm you are while explaining this subject

[@mush4ka]

I didn't need to learn this, but I don't regret learning this.

[@user.name.numbers.letters]

Used this in class today in an activity where you had to make the bigger number out of a limited number of popsicle sticks. I made a 7 and tetrated? It to the fourth. (Idk if tetrated is the right term). The teacher thought I made it up, I showed him this video, he was super impressed.

[@PrimeNewtons]

That was a huge number you made.

[@3bypi]

good job bro

[@estellejones6233]

consider: 4^^7

[@jamx02]

This number is 1 followed by 10^70,000 zeroes, or 10^10^70,000. This number is magnitudes bigger than a googolplex, and it isn't even close. 7^^4 can be written with exponents, but 7^^^4 is so big there isn't enough space in the universe to write the tower of exponents this creates.

[@estellejones6233]

@@jamx02 4^^^7

[@kima.6611]

Somehow your videos have never come across my feed or my search results before. I really enjoyed everything about this video and yourself. I subbed not only for the aforementioned reason, but the sound of the chalk tapping on the blackboard made this GenXer's heart skip a beat!

[@sharikahasan5495]

Bro taught us how to live by loving numbers in billion language,,,this kind of teachers are who we maths lovers crave for!!! If only I can fulfil my dream of pursuing Engineering, I'll surely try to make these type of good stuffs for ppl,,,this type of content is much needed in the south asian part of ours.

[@michaeladams2291]

It has been a long time since I’ve needed to process information in this way and I didn’t realize how much I missed it. Thank you so much and I will be watching all of your future videos. You are amazing.

[@TheTroupeMasterGrimm]

I find it crazy that something as simple as tetration isn’t taught because it’s “unnecessary” but high level calculus and algebra is a part of our curriculum.

[@mikechappell4156]

There are a lot of real world uses for algebra and at calculus for multiple sciences and engineering. Tetration doesn't sound like it has any practical uses outside of advanced mathmetical theory.

[@TheTroupeMasterGrimm]

@@mikechappell4156 even so it’s way more simple to understand, it was just taught to you in basically 5 minutes, one lesson from one math class would be more than enough to satisfy the need. It’s not about replacing them or which one is more useful, it’s about the time it takes to learn. Advanced algebra takes multiple weeks and moths of learning to to fully grasp, maybe even multiple years of the class, tetration took you maybe 5-10 minutes to fully grasp how the concept works.

[@thepiratepeter4630]

@@TheTroupeMasterGrimm The purpose of school is teaching potentially useful information, not cool trivia. Sure, tetration by itself doesn't take a lot of time to teach, but there is an infinite amount of unuseful stuff that takes little to learn, and there is no particular reason to pick tetration among them.

[@TheTroupeMasterGrimm]

@@thepiratepeter4630 but tetration is useful. Not only for writing large numbers but (as the first guy said) for mathematical theory with large numbers. He argued that algebra was more useful since it’s used in “multiple sciences and engineering” which is true, but those only came about due to mathematical theory. In fact, algebra itself is based upon theorizing answers to questions that don’t have them, and then proving those answers. Tetration is useful and easy to learn, and there is no reason it SHOULDNT be In the curriculum.

[@thepiratepeter4630]

@@TheTroupeMasterGrimm Very large numbers, beyond what can be represented with exponentiation, appear rarely in mathematical theory, and never at high school level math. You will never actually use tetration unless you do math research, and even then just in some fields, so there is no point in teaching it. If you wanted to add stuff to the curriculum, there is a lot of better candidates, like some fundamentals of linear algebra.

[@ThePrintZone123]

16, 2x2 = 4, 4 x 4 = 16

[@FreeAmericanSpirit]

Why is it not 2x2=4x2=8?

[@ThePrintZone123]

that would be 2 to the 3rd power this is the third tetrate of 2@@FreeAmericanSpirit

[@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?

[@nunyabiz2117]

​​@@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

[@abrahamben-dayan9843]

@@FreeAmericanSpirit Step 1: 2 to the 2nd power = 4. Step 2: 4 to the 2nd power = 16

[@Jaiden-m3d]

Another notation of the tetration problem "2 to the 3rd tetration" is 2^^3. So, to solve it, you start from the top. 2^2 = 2*2=4 2^4 = 2*2*2*2 = 4*2*2 = 8*2 = 16 2^^3 = 16 *2 tetrated by 3 is 16.*

[@justine.3416]

now imagine ³(³2)

[@klatikw]

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

[@klatikw]

The result on my calculator is infinity, not even joking

[@klatikw]

Now imagine 1.8446744e+19 factorial

[@justine.3416]

@@klatikw that's actually insane. tetration is scary

[@klatikw]

@@justine.3416 wait till you find out about pentation

[@melihhabip]

You must be such a good math teacher, so patient and clear

[@MANOJKUMAR-yk8rc]

It is 16. Really impressed. Saw this concept for the first time in my life. 2 raised to 2 raised to 2 or 2^4 or 16.

[@vishwajeetkumar1858]

16, i am from India. What a great method to express a great number. It is amazing.....❤

[@M.N.Baxter]

You just help me out so much on my thesis paper. I had no idea this was a thing and I’ve been coming up with this in my equations and I didn’t know what it meant. Thank you so much.

[@disappointedbutnotsurprised17]

What's your thesis about? Are you a genius or something lmao

[@M.N.Baxter]

@@disappointedbutnotsurprised17 Nah not a genius, I wish college would be easier for me, lol. I am a student studying mathematics, physics, chemistry and philosophy.

[@moysevii]

2^(2^2) = 16 2^2 = 2x2 = 4 2^4 = 16 You've explained it well 😁

[@Yashraj_Singh_Chauhan]

This thing has increased my curiosity in the world of maths.

[@DeltaPi78]

I was looking at big numbers and came across this term, so I reaserched into it for like 30 min and then realised i had found a whole branch of mathematics i had never seen before. I tried to find when i would be taught this in school but never found it. This means that i will be one of very few in my school to learn this