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.

@TaranVaranYT

6 ай бұрын

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

6 ай бұрын

@@TaranVaranYT yes.

@rsi4054

6 ай бұрын

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

@user-hi8jv6cw8n

5 ай бұрын

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

5 ай бұрын

@@user-hi8jv6cw8n get thx

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

@PrimeNewtons

Жыл бұрын

Yeah. Things get huge really fast here.

@ChraO_o

7 ай бұрын

³2 is 2⁸ or 256

@ChraO_o

7 ай бұрын

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

@Zeoncxtoy

7 ай бұрын

@@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

7 ай бұрын

@@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.

@Jigolopuff

7 ай бұрын

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

@satswak

7 ай бұрын

and also they do not have the feel to teach

@fenidiv4325

7 ай бұрын

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

@Alwaysright42250

7 ай бұрын

​​@@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

7 ай бұрын

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

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

@bwkanimations7352

10 күн бұрын

bro can i retweet

@wendigo7021

10 күн бұрын

@@bwkanimations7352 sure why not

@BickBull

4 күн бұрын

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

@Batmann_

3 күн бұрын

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

@sabretoothc2591

2 күн бұрын

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

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

9 күн бұрын

I hope so too!

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

7 ай бұрын

Thank you!

@pradyothkumarb8330

7 ай бұрын

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

@neevhingrajia3822

7 ай бұрын

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

@Everyoneneedsafriend

7 ай бұрын

​@neevhingrajia3822 i believe it was a joke

@icantcook9998

7 ай бұрын

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

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

@SatyamGupta-hk2gg

5 ай бұрын

The one who stops learning, starts dying

@WeeMasterEmerald

5 ай бұрын

@@SatyamGupta-hk2gg are dead*

@RedSkeletone

4 ай бұрын

that's what I thought

@mr.mystery9338

4 ай бұрын

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

@fredericlaviolette5041

4 ай бұрын

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

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.

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.

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*

@anirchakraborty4953

5 ай бұрын

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

@0xonomy

5 ай бұрын

@@anirchakraborty4953 repeated repetition of the process of repeatedly repeating addition? i dont really know man

@MugsyBogues

5 ай бұрын

@@anirchakraborty4953its pentation

@parthpatel9602

5 ай бұрын

​@@0xonomythanks for making it easy man.

@TheNaz_O5-15

5 ай бұрын

​@@anirchakraborty4953I think it's called pentation, someone in the comments said it.

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.

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 !! 😃

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

@appsenence9244

6 ай бұрын

exceptionally? Don't you mean, expontentially?

@peterproductions5015

6 ай бұрын

@@appsenence9244Smart fella, this one.

@Quvexe

6 ай бұрын

​@@appsenence9244Haha

@ethaniscool315

6 ай бұрын

nice@@appsenence9244

@scottwatts3879

6 ай бұрын

And I'm still looking for him.

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

@JohnFekoloid

7 ай бұрын

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

@Gadottinho

7 ай бұрын

Bruh, math classes are the best

@David280GG

7 ай бұрын

​@@JohnFekoloid😭

@aprilbrandon3441

7 ай бұрын

Noice

@mrkoyunreis

7 ай бұрын

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

now imagine ³(³2)

@MileRancid

7 күн бұрын

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

@MileRancid

7 күн бұрын

The result on my calculator is infinity, not even joking

@MileRancid

7 күн бұрын

Now imagine 1.8446744e+19 factorial

@justine.3416

5 күн бұрын

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

@MileRancid

4 күн бұрын

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

Thank you so much! for teaching us this lesson. It is really something new that maybe very few people actually know and use also.

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

7 ай бұрын

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

@nix_

7 ай бұрын

I got the same answer!

@McSmurfy

7 ай бұрын

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

@SeeltheProgrammer

7 ай бұрын

I understand it now, thanks for the explanation!

@voltznake9248

7 ай бұрын

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

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

@TheOneOtaku

7 ай бұрын

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

@TheDankian1421

7 ай бұрын

EXACTLY.

@TheDankian1421

7 ай бұрын

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

@louiesatterwhite3885

7 ай бұрын

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

@neth7826

7 ай бұрын

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..

Good work sir. More like you would not be any competition and your contribution is precious. All my respect, may God bless you, sir, and your precious two bits in. I say Thanks for all those who won't.

He says "hello! Welcome to another video" with such a warming and calm, friendly voice and a kind smile... just before busting your brain.

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

7 ай бұрын

Glad you liked it!!

@infernoninja5195

7 ай бұрын

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

@mickenoss

7 ай бұрын

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

@Deathwindgames

7 ай бұрын

⁠@@mickenossa fellow dark matter purchaser?

@Kaka_Doctor_91

7 ай бұрын

kzread.info/dash/bejne/l4qGrK59YKuwk6g.htmlsi=fEII6tEEK-zbApDh 👈 At the end of this video you will see the "real life use" of tetration!!

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

16. Not even a big fan of math but this was very relaxing and a great way to explain, I could show a fifth grader this and they'd understand because this video is also disguised as a way to learn exponents too.

That was so funny and interesting! I'm glad I could find your channel, I'm Brazilian and not fluent in English at all, but the way you explain and the fact that math is a universal language did make it easier to me to understand!

@PrimeNewtons

Ай бұрын

Thank you! 😃

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

6 ай бұрын

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

@pannumon

6 ай бұрын

@@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

5 ай бұрын

​​​​@@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

5 ай бұрын

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

5 ай бұрын

the difference between ³2 and ⁴2 is comical 😹

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

7 ай бұрын

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

7 ай бұрын

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

7 ай бұрын

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

7 ай бұрын

​@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

7 ай бұрын

@@dekippiesip my brain is now bigger :D

2 to the tetration of 3 is equal to 2^2^2 = 16.

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

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

7 ай бұрын

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

@Wilson-AM

7 ай бұрын

22 mins ago!

@howtobasic2.031

7 ай бұрын

@@louisrobitaille5810 brudda get to raydons number

@bzibubabbzibubab420

7 ай бұрын

my granpa is graham @@louisrobitaille5810

@Carl_with_a_k_

7 ай бұрын

my personal favourite is penetration @@louisrobitaille5810

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.rection5906

7 ай бұрын

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

7 ай бұрын

@@hugh.g.rection5906 Yes, we do! 😁🤣

Found this in my recommendation, learned something new, was not disappointed. Good work.

It's value is 16... Since, it is (2²)². Because the titration is 3 so we need 3 2s including one in base. So, now we solve it, it will be 2⁴=16.

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

7 ай бұрын

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

@lubomirkubasdQw4w9WgXcQ

7 ай бұрын

no, more like 700 years i think

@magentamonster

7 ай бұрын

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

@davidturizo2847

7 ай бұрын

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

@OJB42

7 ай бұрын

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

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

@UnohanaMash

3 ай бұрын

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

@MoonDark-mq8ex

3 ай бұрын

​@@UnohanaMash😂

@MantoHazra

3 ай бұрын

​@@UnohanaMashHAHA

@loganeliott6590

3 ай бұрын

FR

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 🥲

Based on the well instructed lesson with hints that make you see, the answer cannot be missed. It can be said that raised value number is equal to the base number raised based operation twice, such that ^3 base 2 = (2^2)^2 = 16. So the example given, provided the key information to solve. Thus (10^10)^10 = 10^100. Prince Newton, you are amazing.

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

@bunnybeetle1304

7 ай бұрын

oh cool i got it right!

@ACuriousChild

6 ай бұрын

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!

@Respect_truth_tellers

6 ай бұрын

@@ACuriousChild huh 😶‍🌫?

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

@chimyshark

7 ай бұрын

1.55 billion

@noobiesensei6281

7 ай бұрын

7,62 trillions. This shit is ridiculous.

@CatNolara

7 ай бұрын

actually not that much, only 19,683

@nekro1977

7 ай бұрын

@@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

7 ай бұрын

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

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

Amazing Video! They don't teach this in school but I had heard of it before, thanks for explaining how it works. "Don't stop learning, those who stop learning have stopped living" Such a moving thought! 🤩

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

@Hanible

7 ай бұрын

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

7 ай бұрын

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

7 ай бұрын

​@@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

7 ай бұрын

​@@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

7 ай бұрын

@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? 🤔

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

6 ай бұрын

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

6 ай бұрын

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

6 ай бұрын

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

@Toast_Sandwich

5 ай бұрын

@@astromacheand what of 0?

@astromache

5 ай бұрын

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

This is genuinely one of the craziest things I’ve seen!

This is the first video of your chanel which i have seen. That shows that this channel is for knowledge.

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

@SomeCowguy

6 ай бұрын

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

@PrimeNewtons

6 ай бұрын

That's why I left the system too.

@QUBIQUBED

6 ай бұрын

@@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

6 ай бұрын

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

@SomeCowguy

6 ай бұрын

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

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_Kabbaher

5 ай бұрын

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

5 ай бұрын

what@@Atmatan_Kabbaher

@satgurs

5 ай бұрын

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

@sefutho

4 ай бұрын

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

@jasminerochas-oq8jw

4 ай бұрын

This is a tetration of 2, not of 3.

I enjoyed the setup of comparing the infinitesimally large number to the test question. Nice trick.

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

Ай бұрын

He's correct. That's impressive 😊

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

@ThatOneProFloppaTheBest

7 ай бұрын

i used my calculator it answered 1

@Perrigon

7 ай бұрын

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

@ThatOneProFloppaTheBest

7 ай бұрын

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

@ZenGodXGaming

7 ай бұрын

What r u on

@hycubo

7 ай бұрын

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

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

The answer to it is 16 because it expands to 2^2^2, in other words 2^4. 2^4 is just simply 16.

16 I am a kid from 6th grade. I can understand you, you teach very good😊😊.

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

7 ай бұрын

Not sure where you got "up arrow" from - the character you mean is actually on your keyboard: "^"

7 ай бұрын

@@TekExplorernope, that particular notation uses up arrows, as dictated by the name..

@l3dcobra120

7 ай бұрын

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

@first-namelast-name

7 ай бұрын

​@@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

@Iammankey

7 ай бұрын

Well then what's 3↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑3?

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

5 ай бұрын

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.

A staircase of exponentiation... A tool so powerful we don't have many practical applications for it in our universe! Amazing thank you for sharing!

This is the most epic math video I’ve ever seen hahaha. It’s 16!! I loved watching this!

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

@fullsendmountainbiker5844

7 ай бұрын

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

7 ай бұрын

@@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

7 ай бұрын

@@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

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

5 ай бұрын

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

5 ай бұрын

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

4 ай бұрын

@@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

2 ай бұрын

Do you people still exist?@@scottbenzing1361

The answer is 16. By the way, thank you so much for teaching me this! I never think that I would learn this in school, so thank you.

16, surprisingly simple. 2^2^2 becomes 2^4 becomes 16. I can see why this wasn’t taught in school. I’m still trying to understand it.

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

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

6 ай бұрын

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

@nowherenearby9461

6 ай бұрын

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

@rjtimmerman2861

6 ай бұрын

@@nowherenearby9461 the same as all inventors, a person with an idea :)

@trafficbyintent

6 ай бұрын

Why isn't this hearted ❤

@SAJe_53

6 ай бұрын

So now figure out what's after tetrarion.

Thank you man God bless you❤ for this knowledge which you gave us.😊

16 due to 2^2 being 4 and this result being the next exponential so 2^4 which equals 16.

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

@TelPhi_

3 ай бұрын

fr fr no cap!!!!

@MyOneFiftiethOfADollar

3 ай бұрын

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

@subup4116

3 ай бұрын

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

@ganyu_literally

2 ай бұрын

You ratioed him 🔥

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

6 ай бұрын

"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

6 ай бұрын

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

@ACuriousChild

6 ай бұрын

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

@johnshaw6702

6 ай бұрын

​@@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

5 ай бұрын

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?

my work shown: 2 ] = 2x2 = 4 2 ] 2 ) 4 x 4 = 16 3 2 = 16

Very interesting stuff. Answer is 16 because it is kind of like the power of a power rule on exponent multiplication.

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

12 күн бұрын

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

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

@PrimeNewtons

7 ай бұрын

Lol 😆

Good to see a fellow black guy speaking eloquently and spreading knowledge of maths. It's often a white or Indian. Keep going man 💪

Its 2^4 = 2×2×2×2 =16 I learned it in belgian college (to help calculate big numbers) but the notation was different , we used a special combination of exponents and accolades

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

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

Watching u from India honestly I know nothing about this thank u teacher u taught a new concept 😊

8 didnit! Followed the example and got 16! At school in 1980s maths teacher were never like you! 😊

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

7 ай бұрын

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

@RebelKeithy

7 ай бұрын

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

7 ай бұрын

Then search grahams number hahahah

@dylandillpickle568

7 ай бұрын

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

7 ай бұрын

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

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 :')

2 is such a cool number. It’s also neat how 2 = 2!.

Really nice to see you hearting our comments even though there are so many. Great explanation btw.

@PrimeNewtons

8 күн бұрын

I try 😃

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

7 ай бұрын

im still in highschool, your magic words are scaring me

@TheDiamondPro44

7 ай бұрын

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

@VictorianSnailGod

7 ай бұрын

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

@the_Mousee

7 ай бұрын

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

@mission2858

7 ай бұрын

Time* to go even further ahead in my maths education and work out what the fuck this means.

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

6 ай бұрын

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

16 sir I solved it by own and do many other examples. Thanks sir to taught something new other than schoolwork. Our school teaches what that someone already knew things but not those thingsthat no one find that.

Very nice video, and I like your saying "those who've stopped learning, have stopped living"

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.

2^2^2 = 16. I feel like tetration will be used one day as quantum computers become reality.

@PrimeNewtons

Жыл бұрын

I agree. I believe it's already being used.

This makes me love maths more and more, truly amazing! ❤😊

In the first place it was difficult to imagine what it means. But then I got it. 2^2^2, starting from the top 2^2=4, => 2^4=2*2*2*2=4*4=16. Thanks for widen my horizon.

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

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

@FreeAmericanSpirit

7 ай бұрын

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

@titustech4453

7 ай бұрын

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

@FreeAmericanSpirit

7 ай бұрын

@@titustech4453 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

7 ай бұрын

​​@@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

7 ай бұрын

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

Great video, but let's give some credit where it is really due. Amazing penmanship! How many people can write on a board and both maintain scale and keep everything on a straight line? So pleasant to look at. I think I'll watch it again. 😊

@PrimeNewtons

8 күн бұрын

Thank you

Really loved this lesson, got to learn something new!

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

Nice handwriting

@NotEntirelyStupid

6 ай бұрын

He really does

Just unlocked a memory inside my brain. When I first learnt exponentials, sometimes I solved it as if it were a tretation (I didn't even know it existed until now). Just happened twice, and then I used the exponentials in the right way.

Such a cool concept! Thank you for sharing.

³2 = 2^2^² = 2⁴ = 16. So basically use the first ^2 to raise to the ² power again. It would be the same method as doing 2² but it's on the exponents now with ³2. So the coefficient would be 2⁴ = 2×2×2×2 = 16. Never learnt this in school like learning about how to make money in school😂

@masscreationbroadcasts

7 ай бұрын

How'd you make a small 4? Oooh... I never noticed you could make more than superscript 2 and 3.

@colonelquack

7 ай бұрын

On a android, if you hold down a number, say 2, you'll get an option for ², and other characters. (⅔ and ⅖, apparently)

@vedantsethi7124

7 ай бұрын

​@@colonelquackyou are right 😮

@princ3ss_fschl195

7 ай бұрын

They never teach this because it's never needed. As seen, the numbers are so insanely large that things in the entire universe are much too small to be measured in tetration, so even professional mathematical jobs do not need to use tetration as often.

@misterphmpg8106

7 ай бұрын

you never learned how to make money at school because if teachers knew how to make money they wouldn't be teachers 😳

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!

i have understood this concept from this random man at 3 30 am on yt faster than i ever understood a concept in the whole of school and the answer is 16 and i very much understand why he said they get out of control, very fast

the answer for the question is 16 and if we do it 3 tetrated by 3 then the answer becomes 19683. This is really uncontrollable.