Math - Addition, Multiplication, Exponents, & Tetration

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This mathematics video tutorial provides a basic introduction into addition, multiplication, exponents, and tetration. Addition can be thought of as repeat counting. Multiplication is repeat addition and exponentiation is repeat multiplication. Tetration is repeat exponentiation. This video explains how to find the value of a number raised to the super power of another number. It also explains how to find the super square root and the super cube root of a number.
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2 июл 2024

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Комментарии : 234

@TheOrganicChemistryTutor 5 месяцев назад

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Math & Science Videos: www.patreon.com/mathsciencetutor/collections

@s_naeemnaqvi8725 4 года назад

I've been doing math for years and its the first time I'm hearing about this stuff

@billr062 4 года назад

Me too

@udith 4 года назад

🖐️

@alberteinstein3612 3 года назад

Same

@JamesJones-cm6vi 3 года назад

Yea me too

@4c029 3 года назад

Me too, this is the first time I've ever heard about addition (this a joke btw)

@element1192 Год назад

You can extend the sequence of operations to create as many operations as you want. Counting (the successor function) -> addition (iterated successor function) -> multiplication (iterated addition) -> exponentiation -> tetration -> pentation -> hexation, etc. It's called the hyperoperation sequence. The only practical use for hyperoperations higher than exponentiation that I can think of is as a means of expressing numbers so large that scientific notation doesn't suffice.

@JeanpierTameuina2024 8 месяцев назад

I got it to heptation

@Hello-kr8gj 8 месяцев назад

Thanks for this video it is the only one I have seen on tetration that actually explains simply what it is and in a way that anyone could understand immediately in seconds.

@marcwilliams9824 8 месяцев назад

This helped me ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eVRJLD0HJcE.htmlsi=XLuL-gi7GIQG6NBO

@erodey3133 4 года назад

Omg dude, I've been thinking of this concept in my free time, but didn't know how exactly tetration, now I know, is called. I googled it, but no result, thank you mate

@aweebthatlovesmath4220 2 года назад

No way same to me i was 14 and this came to mind

@georgesadler7830 2 года назад

Professor Organic Chemistry Tutor, thank you for a fantastic video/lecture on Mathematics Operations. I have seen all the classic Mathematical Operations throughout all levels of Mathematics and Engineering, however Tetration is an operation that I have never seen or used. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.

@argonwheatbelly637 4 года назад

A most gentle explanation. Lovely, this.

@Jo_Es_Chess_Channel 4 года назад

First time I even hear of tetration... Cool concept! Edit: How can you use retraction with decimals like 0.5?

@ShadowVipers 4 года назад

Same here

@Jo_Es_Chess_Channel 4 года назад

@@account5223 3:09 blame him

@jhonlawrencebulosan741 4 года назад

If you think this is cool, learn arrow notation. It basically uses the same concept, except writes it in a different notation. The reason for the different notation is to keep stacking the operations, so it starts with one arrow meaning exponents, then two arrows for tetration, then 3 for the operation after tetration, then so on. I think the main use for arrow notation is for the humungous ginormous number named "grahams number". If you're interested for more information about this number and the arrow notation system, I suggest watching numberphile's video about "Graham's Number"

@Jo_Es_Chess_Channel 4 года назад

@@jhonlawrencebulosan741 thanks!!

@harryw4802 3 года назад

approximations can be made.

@colorx6030 3 года назад

Wow, this was never taught to me. I'm glad I explored your algebra playlist!

@Zantofez 8 месяцев назад

Great video, watched it just out of interest and you kept it nice and simple!

@annlaubstein2781 10 месяцев назад

Your videos are amazingly helpful😊

@euskedyzestoa2008 6 месяцев назад

I love it! I knew my mistakes in middle HS will come to be real stuff as of this Tetration ONE OF THESE DAYS!! I knew I knew!!

@McFlashh Год назад

Best maths channel on RU-vid

@Flamerate1 4 года назад

I just realized that every higher power function involving 2 and 2 will equal 4. I'm not sure if that means much, but... 2 plus 2 = 4. 2 times 2 = 4 2 to the power of 2 = 4 2 to the superpower of 2 = 4 etc.

@shreechaturvedi4170 4 года назад

that is wayy too awsome underrated comment btw

@Xonatron 2 года назад

They all mean 2+2. Or rather, 2 incremented twice (successor). It’s cool to think of how they propagate downward.

@Lou-uj6my 8 месяцев назад

Thank you, this was very interesting

@memetank3569 4 месяца назад

Great explanation

@donut2676 3 года назад

math got hard when alphabets got involved and now they have super powers

@ismailabdelirada9073 6 месяцев назад

It gets really interesting when the Greek alphabet comes in.

@sel8015 4 года назад

Thank you sir

@mgtowvalues Год назад

Excellent.

@bill-nn1vp 3 месяца назад

good vid!!

@JeanpierTameuina2024 8 месяцев назад

All Math Levels: Level 0: Succesion: a + 1 Level 1: Addition: a + b = a + ... + 1} = (b × (a) + 1)) Level 2: Multiplication: a × b = a + ... + a} = (b × (a) + a)) Level 3: Exponentiation: a ^ b = a × ... × a} = (b × (a) × a)) Level 4: Tetration: a ^^ b = a ^ ... ^ a} = (b × (a) ^ a)) Level 5: Pentation: a ^^^ b = a ^^ ... ^^ a} = (b × (a) ^^ a)) Level 6: Hexation: a ^^^^ b = a ^^^ ... ^^^ a} = (b × (a) ^^^ a)) Level 7: Heptation: a ^^^^^ b = a ^^^^ ... ^^^^ a} = (b × (a) ^^^^ a)) Level 8: Octation: a ^^^^^^ b = a ^^^^^ ... ^^^^^ a} = (b × (a) ^^^^^ a)) Level 9: Ennation: a ^^^^^^^ b = a ^^^^^^ ... ^^^^^^ a Level 10: Dekation: a ^^^^^^^^ b = a ^^^^^^^ ... ^^^^^^^ a} = (b × (a) ^^^^^^^ a)) Level 11: Hendation: a ^^^^^^^^^ b = a ^^^^^^^^ ... ^^^^^^^^ a} = (b × (a) ^^^^^^^^ a)) Level 12: Dokation: a {10} b = a {9} ... {9} a} = (b × (a) {9} a))

@zanemiracle6121 4 года назад

"If you put this into a calculator you're going to get an error" Me: Challenge accepted! *Puts into Ti-36X pro* Ti-36X pro: *OVERFLOW ERROR* Me: No more playing around *Puts 2^65,536 into TI-nspire cx CAS* TI-nspire cx CAS: You underestimate my processing power *Returns Infinity* ! Me:...but that's just....well played.

@yatogami7393 4 года назад

Mine returned some large exponential value (precisely 2.003529930406846464979072351E19728) But if you take a six figure rather than this five figure , it gives infinite. Phones give a timeout .

@solidwaterslayer 4 года назад

@@yatogami7393 wft calculator are you using? e19000??!?? thats insane

@shreechaturvedi4170 4 года назад

underrated

@donovanj.528 4 года назад

Who's just watching this cuz they're bored?

@EmporiumOfMissiles 4 года назад

hi bored

@yatogami7393 4 года назад

Only u , I guess

@user-vs1mn8ig8w 4 года назад

@jjmmm515 3 года назад

@@yatogami7393 probably dv 2

@bishwaroopbiswas286 2 года назад

@deEscapion 4 месяца назад

For the first tetration question, the approximation at the -illion scale can be expressed like this: 2 sextimilliquintigentiquinseptuagintillion.

@huixing888 3 года назад

Tetration can also become defined as a row of E. (only if the left side is 10.) (10^^3)^50 would format easily as = eee50 or E50#3.

@Xonatron 2 года назад

Can you break that down for me a bit more?

@thorstenbrandt8739 8 месяцев назад

What is E? I know it only for error on my calculator.

@williamwilting 2 месяца назад

How is an inversed operation of a level higher than tetration written down? Are there 2 S's with a super root of inversed pentation, or '(S+1)', or 'S^¹', or something like that?

@qtnico2198 4 года назад

i love dis dud

@JustAPersonWhoComments 8 месяцев назад

In short: Exponents: 2^4 = 16 Tetrations: 4 tetration of 2 = 2^2^2^2 = 256

@Manager_Mister 4 года назад

12:48 p and i should be sleeping. But even in my dreams i never would have heard of S. I love it.

@sendansen7416 8 месяцев назад

7:16 why do you put a comma in the integer?

@azael532 4 года назад

Thank you kind sir. I'm in 8th grade and I'm taking Algebra 1. If you could teach more about Algebra 1 so I can be prepared for my finals that'd be great :). Or Algebra 2 :)

@herobrine8763og Год назад

Hows 11th grade going?

@azael532 Год назад

@herobrine8763 crazy cuz I ain't doing no more math since I got all my math credits and I took geometry, honors alg 2, college algebruh, and dual pre cal and even took my S.A.T and got pretty decent scores What a journey

@KronosAnimates 9 месяцев назад

sheesh what a development

@jessamariemangubat406 4 года назад

Wow I have encountered these equations just now 😱

@EnderSand2486 8 месяцев назад

What about the opposites? (Subtraction, division, and un-tetration if that’s a thing)

@rajendraraut841 4 года назад

Nice

@sejal3163 2 года назад

bruh ive been thinking of this concept and i thought i was sooo smart until i realized it alr exists

@lyl380 8 месяцев назад

😂it’s all good though. The fact that you thought and most people never did, shows your minds cogs are above average.

@seeforkat 3 года назад

stages of the reconstructor

@Azimsultan919 3 месяца назад

5:04 - tap • 10^

@FlRElNTHEHOLE-69 8 месяцев назад

I have one wish. And that wish is for people to not forget about this symbol!!! -> ^

@ahmedabdelkoui3790 8 месяцев назад

We can say that an odd number raised to a power remains odd and an even number raised to a power other than zero remains even and therefore 2^5 is not equal to 5^2.

@mimikyubutitsactualyhornet 8 месяцев назад

What about sucetion? It's below addition becuse sucestion is (any number)+1

@ogeidnomar4601 2 года назад

How does Pentation work? I try to imagine how iterated tetration may function, but I can't seem to get a grasp. There's hardly any info on anything above Tetration online.

@KingTheRat 2 года назад

Look into Donald Knuth's up-arrow notation. Same concept with different notations. There's a good wikipedia article on it.

@ogeidnomar4601 2 года назад

@@KingTheRat I came across another video that clarified it. It's easier than I thought. I was just confused about anything above Tetration since hardly anyone really discusses anything above it. At least where I search.

@user-seg-ubffzlf 8 месяцев назад

3^5vs5^3

@megatronikal8853 6 месяцев назад

Also (3³)³ equals 3⁹ because (x^y)^z=x^(yz)

@nangoloruusa3971 4 года назад

How do you press super power or super root on the calculator?

@thebestnoob9958 2 года назад

sadly,there is none of super power and super root on a calculator

@saravanankabilanm5975 2 месяца назад

very shocked but so interesting

@sjoerdstougie 2 года назад

'have you ever wondered what the difference is?' no because i havent ever heard of tetration before

@xxnotmuchxx 4 года назад

The notation i use is 3^3^3 = 3^^3. Can u have something like 3^^2.5?

@waterpidez6732 3 года назад

Idk but ig if u can have 3^2.5 then it should be possible

@gforce97 Год назад

i would assume the answer is somewhere between 27 and 7,625,597,484,987 or 3^27 lmao😅

@robertveith6383 8 месяцев назад

@@waterpidez6732 -- This is not partial texting.

@epicperson-od2hy 4 месяца назад

3↑↑2.5 ≈ 1293

@electrolitdecharmander3555 6 месяцев назад

1:43 Look at the blue rectangle and shake your phone, see how it gives the illusion of it moving lol.

@riwjr 3 года назад

Can there be a tetration Power tower? Like 3 3 3

@gagietrain6438 3 года назад

Oh God.

@AlphaMC 3 года назад

that is called pentation, aka power tower feeding frenzy don't talk about it... *decitration*

@style_was_not_taken 2 года назад

this may be how pentation works, but idk.

@gforce97 Год назад

that means its 3^^7,625,597,484,987 which is going to give you an extremely large number with who knows what number of digits😮

@aweebthatlovesmath4220 2 года назад

When i was 14 i thought i was first person who come up with this lol

@uchennaholder7983 3 года назад

Why is it that during school they teach this stuff, but its so hard to understand vs youtube, you can learn it in less than 15 minutes

@orangexylem 3 года назад

Probably because youtube videos don't have to tell someone to shut up every 15 seconds.

@grahamnewton4381 4 месяца назад

I’m a long way off stupid so a few minutes of this video and I get the principle. I watched a number of other videos before this and was non the wiser. Why when something can be explained in simple terms do so many people want to make sound so much more complicated?

@milestailsprower4555 Год назад

Tetration is used for... Well BIG NUMBERS!

@Freun 8 месяцев назад

Why is my brain wants to watch this math lessons video instead of school🗿

@ArupRoy_fromPlanetEarth 4 года назад

you just forgot to put "s" at the end for the super root of 7.6 trillion

@robertveith6383 8 месяцев назад

@ New Algebra Playlist -- 2*5 does not mean 2 + 2 + 2 + 2 + 2. It means 5 + 5. The number in front tells how many copues of the second number are to be added.

@polymations 6 месяцев назад

2*5 = 2+2+2+2+2 = 10 5*2 = 5+5 = 10 the first number is multiplied by the second number, although switching the numbers give the same result.

@felipecardope 11 месяцев назад

now I know why the first number I see in tetrational madness (idle game) has an F in it, F to pay respects to how big this number is

@userhomer 8 месяцев назад

4:58 i typed it in my phone calculator and no error it typed it in scientific notation

@VladVideos0 8 месяцев назад

2^^^^2=4

@derekritch4360 11 месяцев назад

It is bigger than 10^19000

@user-XxneveralonexX 8 месяцев назад

2.00352993E19728 5:05 trust me i needed a calculator for that

@sahilhossain8204 7 месяцев назад

Lore of Math - Addition, Multiplication, Exponents, & Tetration momentum 100

@SmolDummy263 Год назад

Answer: x = 2

@mathewrafton2904 8 месяцев назад

The titration answer has ~20000 digits

@Nikioko 8 месяцев назад

1:05: You did it wrong for multiplication. Multiplication is multiplicand times multiplicator, while the multiplicand determines how often you add the multiplicator. Thus, 2 ⋅ 5 = 5 + 5 and 5 ⋅ 2 = 2 + 2 + 2 + 2, not the other way around. You can memorize this as 🍎+🍎+🍎 = 3 ⋅🍎, not 🍎⋅ 3.

@astudent8475 Год назад

Let's talk about Addition: ''OK'' Multiplicatiion: ''OK'' Exponentiantion: ''Oh God. Good Night''

@teesteak 6 месяцев назад

25 vs 52

@muhammadsabih8271 6 месяцев назад

I am a sixth grader who's hearing this stuff, I would say that tetration is the black magic of math. Bro, dont even think about getting the final answer or else your calculator would explode. If I be honest, only GOD would get the final answer. Its just too big.

@brettjennizartman4596 8 месяцев назад

2⁵ vs ⁵2?

@gothicbagheera 8 месяцев назад

You misspoke when you said that "729 times another 27 is 19 thousand 6 hundred *_AND_* 83" Putting the 'AND' in there changes the number to 19,600.83 instead of 19,683 (i.e. 729 × 27) And the exact number 3^27 is equal to is 7,625,597,484,987 (i.e. 7 trillion 625 billion 587 million 484 thousand 987) If you want to write 3^27 is approximately 7.6256 × 10^12 don't write =7.6256 × 10^12 write ≈7.6256 × 10^12

@beatakedziora5 3 года назад

5 to the super power of 2 is accually 2.0035299....×10 to the power of 19728

@alop3184 2 года назад

That's 2 to the super power of 5. The order matters.

@Xonatron 2 года назад

Why is tetration repeated exponentiation right to left and not left to right?

@Xonatron 2 года назад

Copying a reply to @GeneralPatton88's thread that got onto the same topic: I think I figured it out, why exponentiation evaluates from right to left instead of left to right: It's because right to left is not repeated exponentiation as it can be simplified. Keeping it simple for a comment (dive into this more yourself): a^a^a if it was (a^a)^a is the same as a^(a*a) or a^a^2... so therefore it makes no sense to do it this way. I dove into the maths much deeper than what I have shared here, but this is not something I have ever heard explained before.

@element1192 Год назад

There actually isn't one standard notation for hyperoperations further iterated than exponentiation. A left superscript is just one of the most simple ways to indicate a tetration expression.

@gforce97 Год назад

you wouldnt evaluate the base and the exponent first when the exponent itself has its own exponents and possibly their exponents have exponents too lmao

@Xonatron Год назад

@@gforce97 Yeah, that makes complete sense too!!

@KingLarbear Год назад

8:20 you should of added in here that 3 cubed cubed is really 3 to the 6th power because when you take a power to a power you add the exponents and so 3^6 does not equal 3^27

@zackvesacisa4164 2 года назад

4:26 😹lol trying to simplify he almost went back to the original 2^16 😹so he said just use a calculator 😹

@aweebthatlovesmath4220 2 года назад

Math is not about only calculating

@K8_r 8 месяцев назад

10:20 why did you add" s"

@K8_r 8 месяцев назад

Another question: 11:20 it can be both positive and negative like for an example tetration of -2 is equal to 2 if the super power is even

@rogergperson 8 месяцев назад

Give him 3↑↑{10} (that’s 10 followed by more than 1b zeros)

@KingLarbear Год назад

I like how at 1:17 you start using different ways to write the number two, to confuse people more lol

@user-rx5dh4le5x Год назад

Whats 3^^1/2? 🤔 I believe 3^^1/2 is equal to 3^1/3

@user-rx5dh4le5x Год назад

Why? Take for example this X^^2(1/2) = x^^(2/2) X^^(2/2) = X^^1 which is = X So x^^2(1/2) = x^^1 Now we take the integer 2 from the fraction and turn it into his potential expression: (X^X)^^1/2 = x Now if we transform the fraction 1/2 into an exponent expression we would expect it and the integer to cancel out to become 1 so it matches the other side of the equation, a simple way to achieve this is by making it the reciprocal of the base like this (X^X)^^(1/2)=X^X(1/X) =X ✔️

@user-rx5dh4le5x Год назад

Basically x^^1/2 = X root of X

@epicperson-od2hy 4 месяца назад

3↑↑0.5 ≈ 1.7068

@crowreligion Год назад

So what is 2↑↑0.5 ?

@CitadelOfVoid Год назад

I'd assume you find the square root of 2. Then 2^sqrt(2)

@serulu3490 Год назад

2^^0.5 = x (2^^0.5)^^2 = x^^2 2 = x^x In(2) = xln(x) ln(2) = (e^ln(x))(ln(x)) W(ln(2)) = ln(x) x = e^W(ln(2)) So 2^^0.5 is approximately 1.5596

@epicperson-od2hy 4 месяца назад

@@serulu3490 you cannot multiply tetration heights. For example, (2↑↑3)↑↑2 is not equal to 2↑↑6. So, (2↑↑0.5)↑↑2 is not equal to 2.

@epicperson-od2hy 4 месяца назад

2↑↑0.5 ≈ 1.45878182

@ToanPham-wr7xe 8 месяцев назад

😮

@KingLarbear Год назад

I have never seen the expression on the right

@jonnaking3054 8 месяцев назад

would rooting be repeat division?

@opgamer1572 8 месяцев назад

why was this even created

@neelam1857 4 месяца назад

Nice question😂

@hajimenagumo2199 Месяц назад

I'm not even in college. I just wanted to know what the hell this was.

@jneal1347 2 года назад

PH(TEMDAS)

@element1192 Год назад

The "emdas" part is just a way of saying "operations are to be performed in descending order of iterations"

@TotallyTaliton 2 года назад

2^^4

@TotallyTaliton 2 года назад

2^^2^2

@TotallyTaliton 2 года назад

2^2^2^2

@TotallyTaliton 2 года назад

2^2^4

@TotallyTaliton 2 года назад

2^16

@TotallyTaliton 2 года назад

65536

@JestWett 8 месяцев назад

so, tetration is like this ³2 = 8 BUT ³3 IS 7 FUCKING TRILLION 💀

@solidwaterslayer 4 года назад

before watching video 2 tet 5 is 2^2^2^2^2 edit: yes im not that dumb

@limehello1797 Год назад

2 years olds cannot understand addition 6 years olds cannot understand multiplication 8 years olds cannot understand exponents 10 years olds cannot understand tetration 12 years old cannot understand you