Tetration equation

[@REHAN._.450]

That smile will attract anyone

[@l.w.paradis2108]

Best math teacher on KZbin. 💯

[@The_Soul_King]

Your way of learning is amazing. You explain everything clearly, and you're always smiling, I would love to have you as my prof I'm only in the equivalent of high school but I understand (almost) everything !

[@arthurvinicius2523]

Man, your voice is just so relaxing, it's just like ASMR and how u explain, th enthusiasm, anyone really enjoy and learn in a math class this way

[@akshajgorugantu666]

Awesome video, i've become a fan of yours now, you're teaching is very addicting and awesome Sir❤

[@tjat55]

your videos are anti-stress, I became a fan.

[@johnfox9169]

Wonderfully motivated explanations. You are the man!!

[@Majan-v8K]

You are gpod, I like your presentations and explanations. Ypou make it in such an easy way zhat any pne can inderstand.Thats teachinh.

[@utkarshpathak3472]

bro really love your videos.... I mean really now I'm doing flax in my college by telling everyone about tetration🤣🤣🤣🤣

[@theking2000]

Nice and refreshing video .. great job

[@adw1z]

Excellent! I love ur videos so much, thank you

[@PrimeNewtons]

Glad you like them!

[@twinkletoes1588]

Maaan you are awesome!! Love from Russia❤

[@BartBuzz]

One question you didn't answer is "What is the practical use of tetration?" I would have imagined that 3††4 is a very large number. But my calculator says that 3††4 is not a number.

[@tatecrossette2855]

Your handwriting is gorgeous

[@PrimeNewtons]

Thank you so much 😀

[@tatecrossette2855]

@@PrimeNewtons I've showed tetration to my math teacher. She has never heard of it. Math theory and just big math I think is the most fun thing to learn about. Thank you!

[@KevinJB1966]

Loving your videos. Your teaching style is unique, and very enjoyable. I hope that your clue about "many arrows" is going to be a Graham's Number video. I've yet to see one that I fully understood but I think if anyone can make it clear, it will be you! I also wanted to ask: you showed that 0 and 1 are solutions to 3^^x=3^x but is there an algebraic solution to this type of question? e.g. can we solve something like 2^^x=9^x?

[@PrimeNewtons]

Thank you. I tried an algebraic solution but it was not helpful. Looking for a better way. I would consider superlogarithm and super roots. I hope I can.

[@aguyontheinternet8436]

well for that example, yes. x=0 is a solution, and if you graph it, I suspect there's a second value in-between -1 and 0 (something like x~-0.843), and a third between 3 and 4 (something like x~3.62), but these would require a proper definition for tetration of real numbers to properly represent.

[@jirisykora9926]

Gorgeous! Keep it up! Soon you'll have like milion subscribers :D

[@surendrakverma555]

Very good 👍

[@enambhuiyan2733]

Doing fun at the same time doing math.❤

[@khemmath]

Nice ❤

[@mr.mxyzptlks8391]

I appreciate the content. Love your calligraphy 🤩What chalk are you using? Now, having ventured into power towers, is there an equivalent into logarithms? I am curious, because all this extends beyond my CS MS classes, long ago…

[@mvpAXEL]

very very generous ❤ love learning 💜

[@OlakokaJoseph]

Credible 🎉🎉🎉

[@aguyontheinternet8436]

Before watching, is tetration even... properly defined for non-integer values? I remember a video from SoME that went quite in depth about it, I'll have to rewatch it, but til then, I know x=0 and x=1 are two solutions to this. as n↑0=1 and n↑↑0=1, similarly n↑1=n and n↑↑1=n. Perhaps there are other solutions that come up when you properly define tetration in the reals. 4:36 nice fix lol

[@ryanman0083]

Yes it is. For a^x = a^^x 0 ≤ x ≤ 1 We can better understand using super Logarithm (inverse of Tetration) By definition sLog2 (2^^3) = 3 NOTE: "sLog" is a notation for super Logarithm. Like how Logarithm cancels the base leaving the exponent ex. Log2 (2^3)=3 super Logarithm does the same with Tetration. We can use super Logarithm to solve non integer super powers since super Logarithm is repeated Logarithm by definition until the result is less than 1 Let's let sLog2 (16) = 3+x Where 0 ≤ x < 1 (represents a decimal) sLog2 (2^^3) = sLog2 (2^2^2) => Log2(2^2^2) = 2^2 => Log2(2^2) = 2 =>Log2(2) = 1 At this point we've taken three logs representing our integer part of the solution (given by the fact that the answer is equal to 1). We just take log again for the decimal x to see what happens to the remainder of 2's that we need. Log2 (1) = 0 Thus sLog2 (16) = 3+0 = 3 Well look what happens when we go backwards through the same process Log2 (Log2 (Log2 (Log2 (16)))) = 0 Log2 (Log2 (Log2 (16))) = 2^0 Log2 (Log2 (16)) = 2^2^0 Log2 (16) = 2^2^2^0 16 = 2^2^2^2^0 = 2^2^2 = 2^^(3+0) The remainder adds an extra '2' to the top of the power tower and the additional 2 is raised to the power of the remainder For 0 ≤ x ≤1 By definition sLog a(a^^3+x) => a^a^a^a^x By definition of Tetration a^^3+x = a^a^^2+x = a^a^a^^1+x = a^a^a^a^^x a^a^a^a^^x = a^a^a^a^x a^a^a^^x = a^a^a^x a^a^^x = a^a^x a^^x = a^x by definition For example take sLog2 (20) = 3+x Log2 (Log2 (Log2 (Log2 (20)))) = 0.1088761602 Log2 (Log2 (Log2 (20))) = 2^0.1088761602 Log2 (Log2 (20)) = 2^2^ 0.1088761602 Log2 (20) = 2^2^2^0.1088761602 20 = 2^2^2^2^0.1088761602 = 2^^3.1088761602 So sLog2 (20) = 3.1088761602 meaning 2^^3.1088761602 = 20

[@aguyontheinternet8436]

@@ryanman0083 :O

[@DreamerTheWolfFox]

i feel like including x{2}y (brace notation) and {x,y,2} (array notation) couldve been other good ways to show how tetration was written. I personally really like brace notation for when the arrows get to be a lot, and i like array notation a lot.

[@Lohikaarme1984]

Looking forward for more arrows!! :D

[@militantpacifist4087]

Can you please do super roots? Thank you. 👍

[@elver_galinda321]

Amaizing video, scared for pentation!

[@LilDP]

Like the reading rainbow of Math.

[@GSUPRIYODas]

U need 10 billion subs

[@anubhavsingh5533]

oooo man make more vedios i love them

[@abc4828]

Are there counter-operations like roots and logarithms are to exponentiation?

[@satanicexistentialist6631]

Would a tetration of -1 be equal to exponent of -1 as well?

[@ryanman0083]

a^^(-1) = 0 by definition a^^1 = a a^^0 = Log a(a) = 1 a^^(-1) = Log a(1) = 0

[@Gnome7495]

Nice video

[@electro_]

чел у тебя дар, как тебя приятно слушать

[@ziroplay2100]

Love this moment❤🙃

[@ShubhamYadav-o6d2f]

Make a video on tree of 3 this video was Also nice

[@Harshavardhantej9000]

❤❤❤❤❤❤❤❤❤❤🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉😊😊😊😊😊😊😊😊 0:35

[@tristanmike]

Damn it, got me on the first question. I saw the formula and the first question and said to myself with full confidence, "NO" and the very moment he started saying what the two answers were, I realized what an idiot I am. I should have known better, lol.

[@bill-nn1vp]

3 tetrated to x = 3 to the power of itself x times... so what is 3 pentated to x..? how would you write that?

[@JSSTyger]

Now we're playing with power, SUPER POWER.

[@nurudeennajeem6605]

Great

[@dranandamay]

Can we start by taking ln of both sides?

[@AvrajitGRoy]

loved it

[@mathiaslist6705]

And I'd one and zero will give you always a solution for any natural base. The interesting thing are bases between e^(1/e) and 2 --- probably even between e^(1/e) and e where you get a solution which is not just 0 and 1.

[@tristanmike]

Are you using Japanese chalk by chance ?

[@ReinaldoGarcíaGarcía-p5h]

I saw the magic zero vanshing from left and appearing to the right... Math is magic 😂

[@tamilselvanrascal5956]

🎉🎉🎉

[@georgepaidas1132]

Excellent 👍👍👍. Very cooooooool or better Very C(O^^15)L 😅😅😅😅

[@truthministries6880]

so clear

[@vashon100]

More power! Uh Uh Uh! Tim the toolman would be happy.

[@justafanofalphabetlore]

There’s complex roots of this equation.

[@SERIRUS-c8h]

Thank You!

[@RicoTonetti]

Deze guy is net zo charismatisch als math with menno😂

[@WilliamWizer]

while it's evident that 0 and 1 are answers to the equation, I see no proof that there's no other solutions. only a good explanation of tetration. by the way, there's still another way to write tetration. using conway chain arrow. instead of 3↑↑4 you can use 3→4→2 I prefer this method because, for example, instead of 3↑↑↑↑↑↑↑↑↑4 you can use 3→4→9 (a bit more easy to read even if nobody in his right mind would try to compute it)

[@someweirdstuff1256]

negative tetration powers: time to cause trouble 😂😂😂

[@jakeworral2428]

will smith's long lost brother

[@nicolascamargo8339]

Wow

[@yuriandropov9462]

If x is a real ,does a^x equal to a.a.a......( x-(times))

[@ToanPham-wr7xe]

😮

[@ryanman0083]

The equation 3^^x = 3^x actually has infinite solutions We can understand better with super Logarithm (inverse of Tetration) By definition sLog2 (2^^3) = 3 NOTE: "sLog" is a notation for super Logarithm. Like how Logarithm cancels the base leaving the exponent ex. Log2 (2^3) = 3 super Logarithm does the same with Tetration leaving the super power. We can use super Logarithm to solve non integer super powers since super Logarithm is repeated Logarithm by definition. Let's let sLog2 (16) = 3+x Where 0 ≤ x < 1 (represents a decimal) sLog2 (2^^3) = sLog2 (2^2^2) => Log2(2^2^2) = 2^2 => Log2(2^2) = 2 =>Log2(2) = 1 At this point we've taken three logs representing our integer part of the solution (given by the fact that the answer is equal to 1). We just take log again for the decimal x (the remainder of 2's that we need.) Log2 (1) = 0 Thus sLog2 (16) = 3+0 = 3 Well let's look at what happens when we go backwards through the same process to see what happens to the remainder. Log2 (Log2 (Log2 (Log2 (16)))) = 0 Log2 (Log2 (Log2 (16))) = 2^0 Log2 (Log2 (16)) = 2^2^0 Log2 (16) = 2^2^2^0 16 = 2^2^2^2^0 = 2^2^2 = 2^^(3+0) The remainder adds an extra '2' to the top of the power tower and the additional 2 is raised to the power of the remainder For 0 ≤ x ≤ 1 By definition sLog a(a^^3+x) => a^a^a^a^x By definition of Tetration a^^3+x = a^a^^2+x = a^a^a^^1+x = a^a^a^a^^x a^a^a^a^^x = a^a^a^a^x a^a^a^^x = a^a^a^x a^a^^x = a^a^x a^^x = a^x by definition for 0 ≤ x ≤ 1

[@valentinmontero3957]

A si como existe el supermercado logaritmo existiría la superficie raíz Slog base 2 de 16=3 por que 2^^3=16. Sraiz de indice 2 de 27=3 por que 3^^2=27

[@user_math2023]

Titration

[@justafanofalphabetlore]

Tetration needs an interpolation 😢

[@ilafya]

The solution is x=1

[@soumyadeepbaidya8191]

I thought you gonna solve x

[@Manishkoti0]

X=1

[@althereq3656]

¹3=3¹ Easy

[@ToanPham-wr7xe]

😮