Why it doesn't converge to 3?

Подписаться 1,3 млн

Просмотров 100 тыс.

50% 1

This is part 4 of the infinite power tower
0:00 review
1:26 what does (cbrt(3))^(cbrt(3))^(cbrt(3))^... really converge to?
5:40 the 3 shows up!
6:40 the graphs of y=x^x^x... vs x=y^(1/y)
8:05 a very similar example
9:10 x^x^x^...=3 has no solution but x^3=3 does
Lambert W function Intro: • Lambert W Function Int...
*The Satisfyingly Strange Journey to the Infinite Power Tower*
Part1: Solving x^x^3=2 vs. x^x^3=3 • they don’t teach these...
Part2: Solving x^x^...=2 vs. x^x^...=3 • Infinite Power Tower E...
Part3: Domain and Range of y=x^x^... • Domain and Range of th...
Part4: Why (cbrt(3))^(cbrt(3))^... converges to 2.4 and NOT 3? • Why it doesn't converg...
If you enjoy my videos, then you can click here to subscribe ru-vid.com...
Shop math t-shirts: teespring.com/stores/blackpen...
Support: / blackpenredpen
Follow: / blackpenredpen
blackpenredpen,
math for fun

Опубликовано:

6 июл 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 164

@141Zero 4 года назад

The Lambert W function is a pathway to many abilities some consider to be unnatural.

@dihydrogenmonoxid1337 3 года назад

But will it save padme?

@juandaviolin 3 года назад

¿що ти думал? From a certain death?

@That_One_Guy... 3 года назад

But can it express x as a function of y that's elementary ? 😏

@nol2521 Год назад

@@dihydrogenmonoxid1337 you will fall in love with the lambert w function instead of padme so that question is irrelevant

@andyiswonderful 3 года назад

So, I took 11 semesters of advanced math in college and grad school, and I am constantly amazed at how much I don't know when I watch your excellent videos.

@blackpenredpen 3 года назад

Thank you : )

@leif1075 3 года назад

@@blackpenredpen Why didnt you tskenthe natural log of both sides at 1:26 first?

@leif1075 3 года назад

@@blackpenredpen and the lam ert finctiom anyway? Does anyone actually understand what it means? And it soubds like youncintradict yiurself in the video later when you say cube root of 3 isna solution..Hope you can respond.

@ozzymandius666 3 года назад

@@blackpenredpen Perhaps one day show us a graph of y=W(x).

@shashankambone6920 3 года назад

@@ozzymandius666 just look at the graph of x=y×e^y... that's the graph of y=W(x)....

@MuPrimeMath 4 года назад

Those graphs are really cool!

@bendaniels7346 3 года назад

Love your vids :)

@sharepremium8614 3 года назад

How is ur comment 3 years ago wtf ?

@angelheretic2190 3 года назад

how's your comment 3 months ago?

@AshrafAli-qn3gb 3 года назад

😱😱😱are you Gost

@bendaniels7346 3 года назад

Wait yo what

@juandaviolin 3 года назад

For anyone lost watching comments from 3 months ago: This video was unlisted and its link was put in the description of another video. So, just a few people watched this part 4. Yesterday, Blackpenredpen changed the settings and now it is public. Have a great day!

@shreyan1362 3 года назад

Thanks ,,, i was shocked

@balaramkrishnahanumanthu5869 4 года назад

My mind blew at 5:12 So the issue was transforming the equation to another equation does not work because their domain:ranges are different. What kind of equations can this happen with? Clearly when infinity comes into play, also whenever imaginary roots are possible. But how do you find functions with limited domains? It seems like an easy trap if you don't know this could happen.

@Prxwler 3 года назад

4:43 easy, k = w

@GianniCampanale 3 года назад

🤦‍♂️

@quirtt 3 года назад

@maskedman8368 3 года назад

🤦‍♂️🤦‍♂️🤦‍♂️

@siddharthabhattacharya3787 3 года назад

@@quirtt bhai tu idhar?

@shreyan1362 3 года назад

@@quirtt har jagah se padhte ho kya xd

@leickrobinson5186 3 года назад

That was a brilliant, beautiful explanation. Thank you!

@blackpenredpen 3 года назад

Thanks!

@oskarkrogsgard3014 3 года назад

@@AstroB7 what is going on....?

@frozenmoon998 3 года назад

Very suspicious results, lol. If I wasn't into maths (such as being interested, obviously not super high level), I would probably assume that these things are made up. But honestly, it's super satisfactory even when you consider easy questions and discuss them through as if you were tackling a major problem. So satisfactory, as usual, bprp!

@xandersafrunek2151 3 года назад

When you said "power tower," it made me really happy.

@nou3227 3 года назад

i love how thanks to you i can improve my math skills and im still in 10 grade i started learning complex numbers with you and you inspired me to think out of the box and more abstractly i hope one day i may know at least a fourth of what you know

@revoltoff 3 года назад

Blackpenredpen you are a true inspiration for me, taking a Calc 1 class for my BA bachelor ( Idk why they include it) I have motivation from your videos that I did not have before. I am certain that I will do everything to pass in my class, I am stuggling with some things but your story and your enthusiasm brother blackpenredpen , God will help me on the way to succes hopefully! Thank you for sharing your sweet knowledge brother !

@marcusdecarvalho1354 3 года назад

Unbelievable! Extraordinary! Marvelous!

@soulsilencer1864 3 года назад

Hi, love your videos, can you take the integral from -2 to 2 sqrt(1-x^2) dx ?

@jibiteshsaha4392 3 года назад

Please someone explain me how does the fixed point convergence criteria come How does that interval come

@nafrost2787 3 года назад

10:14 so what you're saying, is that the two graphs (and therefore the two equations) are only equivalent on certain intervals, and 3 is outside of this interval, but this bags the question, how do you find the interval in which the two equations are equivalent?

@vaibhavm2916 3 года назад

Can you pls tell me which company markers do you use.they seem pretty easy to hold 2 in a hand and switch

@ulanluhod9628 3 года назад

HAPPY TEACHERS' DAY ❤️ thank you so much for your videos, I wan't you to know that we really appreciate you and what you are doing ☺️

@LShadow77 3 года назад

Hello! Can you make the video where you get the link between the Riemann zeta function and Bernoulli numbers kind of B(t) = -t*Zeta(1-t). How is it gotten? I triied to get this equotion but I couldn't - only my brain was broken! Thanks, I hope for this video will appear soon...

@angelmendez-rivera351 4 года назад

One can figure that 3 is a value that cannot be converged to because the function f = x |-> x^(1/x) attains a global maximum at x = e in the positive real numbers. Hence if x = 3, then 3^(1/3) < e^(1/e).

@MK-rh4wx 3 года назад

i love how you explain it

@martinhimstedt5130 Год назад

Excellent!

@benisjamin6583 3 года назад

@blackpinredpin Looking fresh as always! Great video.

@omarfawaz1051 3 года назад

Beautiful... Thanks🌹

@jibiteshsaha4392 3 года назад

I am really trying to find the derivation of the fixed point convergence criteria I tried everywhere Didn't find anything Not even in lot of papers Plz someone help me

@efulmer8675 Год назад

For the infinite power tower, I am curious why it doesn't converge at values between 0 and e^-e. I tested 0.05 up to 30 copies of 0.05 and it jumps back and forth between ~0.1 and ~0.7 getting closer towards some value between those two numbers so it seems like it would converge to some specific value. I wonder if values between 0 and e^-e exhibit some kind of bifurcation chaos where they stay finite but bounce between two values and thus diverge in that way.

@asharmasharma51 3 года назад

From India watching you nice concept loved it

@shruggzdastr8-facedclown 2 года назад

Is there a number such that when applied to an infinite power tower it converges on pi?

@magicodabola10 4 года назад

Amazing!

@SuperYoonHo 2 года назад

very nice!

@rateeshk8175 3 года назад

Is three (3) the only misbehaving number in these problems???

@gtziavelis 3 года назад

Well, well, well... excellent!

@peterruf1462 3 года назад

Why does the power tower oscillate if you chose x smaller than e^-e?

@rajmanitiwari5346 3 года назад

I'm in class 12 cbse 2020-21 batch I don't know what's happening but yes it looks cool to solve your questions ❤️❤️🥰

@glendagiron9685 3 года назад

Need your help. What is the answer here? x^x^x^x^... = 10

@georgeb8893 3 года назад

Here is a related problem where cube root of 3 does seem to be the answer: suppose start with a reasonably large number, say 100. Then you start taking log base some fixed number x greater than 1. Then you notice that the more you take log base x the closer and closer it gets to 3. What was the x?

@shashankambone6920 3 года назад

So.. ln(100)/ln(x) = 3? Is that what we are trying to solve? Because that's trivial....

@xinpingdonohoe3978 2 месяца назад

So I suppose the different values for W come out when you use different cube roots of 3. All these multivalued functions are countable, so it should be able to be bijected.

@LUCATRON-hs8cj 3 года назад

Nice song at the end

@fsf471 3 года назад

Holy shit I was just thinking of this earlier did you read my mind?

@tomatrix7525 3 года назад

Wow that function is cool

@gudmundurjonsson4357 3 года назад

dont you also assume the the power tower of x can be written as 3 when replacing it, i.e. assuming it converges?

@mtaur4113 3 года назад

I think that assumption is how you get the false solution. tower = x^tower = 3, and plug in 3 for tower. Well, the tower built from 3 actually diverges toward infinity.

@shashankambone6920 3 года назад

Exactly. That's exactly the problem.

@beltin_time 11 месяцев назад

I came to same equation 3^(⅓k) = k, but then I took ln() of both sides ⅓k ln(3) = ln(k) Divide both sides by k ln(3)/3 = ln(k)/k k = 3 Why is it wrong?

@NekoAlosama 4 года назад

ooh

@shubhampradhan5348 3 года назад

Sir please provide the PDFs of 100 integrals, 100 derivatives, 100 series... Humble request👍👍

@djvalentedochp 4 года назад

Nice

@particleonazock2246 3 года назад

You know you're dealing with advanced math when blackpenredpen doesn't summon the fish.

@oxygen2623 Год назад

1:00 Well, that escalated quickly

@joejavacavalier2001 3 года назад

But how would you calculate W lambert values manually?

@savitsios 3 года назад

Same as the natural log, you basically can't Or with trial and error

@shashankambone6920 3 года назад

@@savitsios i mean there are many ways to approximate....

@jibiteshsaha4392 3 года назад

I asked this in the previous video I want a proof for the fixed point convergence criteria

@i_saidmeow2469 3 года назад

The chomper microphone!

@djttv 3 года назад

Here is a question for you: Given: A=(1/2)sqrt((1/2)(3-sqrt(5))) B=(1/4)(sqrt(5)-1) It can be shown that A=B Question is, given A, how do you turn it into B?

@blackpenredpen 3 года назад

djttv It’s similar to this one ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-afz3t8R34r4.html

@djttv 3 года назад

@@blackpenredpen I learned something new! Thank you

@Bobbius-il9rf 3 года назад

Brilliant XD

@basedblueboy8770 3 года назад

@ 2:20 - when you have (3^(1/3))^k = k, couldn't you take the k-th root on both sides, so the k exponent disappears on the left (k/k=1), and the equation becomes 3^(1/3) = k^(1/k), therefore k=3? where is my logic flawed?

@basedblueboy8770 3 года назад

Edit: just watched the rest of the video, so 3 can be a solution. This is technically a way to solve the problem, but if you solve this way without using W function, the other solutions are not intuitive.

@willyou2199 3 года назад

f(z) = ze^z is not monotonically increasing and thus the inverse f^-1(z) = W(z) is multivalued. Quite easy. Same with sin, cos, tan except those are periodic and easy to understand.

@meiwinspoi5080 3 года назад

cool.

@nafrost2787 3 года назад

This guys is really addicted to the W function.

@JSSTyger 3 года назад

I have a question. Does x^x^x equal x^(x^x) or (x^x)^x?

@Silvar55x 3 года назад

x^x^x = x^(x^x) always. You need parenthesis on (x^x)^x.

@JSSTyger 3 года назад

@@Silvar55x MicroSoft Excel says 3^3^3 = 19683

@Silvar55x 3 года назад

@@JSSTyger Well this video and discussion are about mathematics - not the peculiarities of spreadsheet applications. (There's probably a historical reason those programs do it that way - to not break compatibility with legacy software.) If you're talking about mathematics, "x^x^x" doesn't mean "input this string into Excel/programming language", but the abstract mathematical expression of two exponentiations stacked without parenthesis. Can't really write that as is in these comments. Furthermore, actually (a^b)^c = a^(bc) that is "b times c" in the exponent.

@evanlewis2349 4 года назад

Can’t you just raise k to the 3rd power to get: 3^k = k^3 and solve as if it was x^y = y^x?

@evanlewis2349 4 года назад

If you do it like this, then you get 3^k = k^3 which means k = log3 of k^3 which equals 3* log3 of k and if you repeat this, you get k = 3 * log3 of 3 * log3 of 3 * log3 of... which evaluates to 1? There doesn’t seem to be another solution to k that makes the RHS true :/

@angelmendez-rivera351 4 года назад

Evan Lewis You wouldn't use logarithm base 3, you would simply use the natural logarithm. k^3 = 3^k implies 3·log(k) = k·log(3), which implies log(k)/k = log(3)/3, which is solved by using the Lambert W map.

@logicalproofs7276 3 года назад

Regular videos Woooooow

@omshandilya8888 3 года назад

2020 raise to the power 2019 - 2020 divided by 2020 square + 2021=N then find the sum of digits of n bro plz solve this?? trying from last 5 weeks

@justinlink1616 4 года назад

My head is going to expode.

@vaibhavm2916 3 года назад

I just thought for a moment,why his beard was shorter than usual. But later I realized that this video was shot months before.

@Dear999 3 года назад

Pendyala education and eentertainment 👍

@haval00 3 года назад

How come some comments be from 1 month ago ??

@coc235 3 года назад

This video was available by link

@blackpenredpen 3 года назад

It was unlisted in my playlist

@haval00 3 года назад

@@blackpenredpen Ok thank you , great video btw

@SoWe1 3 года назад

ok I'm stupid why does -2 = sqrt(x) not have any solutions even in the complex plane? i*4?

@aeropoulpe7818 3 года назад

sqrt(4*i) = 2 * sqrt(i) = 2 * ( sqrt(2)/2 + i*sqrt(2)/2 ) = sqrt(2) + i*sqrt(2)

@SoWe1 3 года назад

@@aeropoulpe7818 sqrt(4*i) = 2 * sqrt(i) = 2*(-1) = -2

@aeropoulpe7818 3 года назад

@@SoWe1 no i^2 = (-1) , sqrt(i) is different z = sqrt(i) means z^2 = i so there are 2 solutions : (z = sqrt(2)/2 + i*sqrt(2)/2 ) or (z = -sqrt(2)/2 - i*sqrt(2)/2 )

@SoWe1 3 года назад

@@aeropoulpe7818 rightrightright, yes but still, why does that equation not have any solutions?

@aeropoulpe7818 3 года назад

@@SoWe1 i'm not sure but i would say : - a square root of a complex number (not real) is always is a complex number (not real) - therefore sqrt(x) = -2 only have solutions in R - but sqrt(x) >= 0 in R so there are no solutions at all

@darshanvanjara6009 3 года назад

Integration of 1 /1+secx ..... PLEASE SUGGEST SIR......😔😔😔😔😔😔😔😔☹️

@darshanvanjara6009 3 года назад

@3head individual done sir... THANKS a lot ..

@darshanvanjara6009 3 года назад

@3head individual where are you from sir. Japan??

@ordinary1017 3 года назад

U're the best

@DeadJDona 3 года назад

6:22 how could complex numbers infinite power look?

@saisrirajnallam 3 года назад

Thank u maths teacher

@MeOKMeO 3 года назад

So interesting pardon my naive, Never thought about X^(1/X) when X =3 that (3)^(1/3) equals to when X =~2.478 that (~2.478)^(1/~2.478), indeed wonder how many numbers between that range has two real solutions as pairs🤔, very interesting!

@MeOKMeO 3 года назад

Downloaded a curve equation generator, between 1 and e

@shashankambone6920 3 года назад

How many numbers? Infinite....

@aryanbhargav9705 3 года назад

Now I am in future

@lupusofaquarius7434 4 года назад

Your pens surely hold infinite power!

@Silvar55x 3 года назад

@Ajay singh Video was unlisted for ~3 months, but with link provided in the description of a previous video in the series. That's how some people could find it before it was published a few days ago.

@GammaFZ 3 года назад

whatislambertwfunctionpleasemakeavideoonthatthanks

@TecknoVicking 3 года назад

🔒

@swampman4204 3 года назад

Hello bprp!!!!

@lawrencebermudez 4 года назад

e = 3

@satteshwaribharti9524 3 года назад

Hi.. I have a challange question for you.. 😂😂

@wallissoncoelho7451 3 года назад

How do you learned English?

@chinjunyuan1720 3 года назад

@gordonchan4801 3 года назад

henlo

@aryangupta904 3 года назад

Hey man Cube root of 3 to power cube root of 3 Infinite times Let it be x Cubing both sides 3power cube root of 3 power cube root if 3 Infinite times=x³ Dividing both sides by 3 1power cube root of 3 Infinite times=x³/3 1=x³/3 X³=3 X=cube root of three Solved.

@shashankambone6920 3 года назад

Wait what? You must be joking.....

@ipetmycats99 3 года назад

how did I get here

@estelle_chenxing 3 года назад

@jacobhall4655 3 года назад

0:27 not according to physicists

@oscartroncoso2585 3 года назад

First!

@ssdd1316 3 года назад

@purim_sakamoto 3 года назад

うーん　むずかしかった

@purim_sakamoto 3 года назад

3週間ぶりにようやく理解しました😀 こりゃ学部1年終えるのに8年かかっちゃうね😭😭

@gurkiratsingh7tha993 2 года назад

Technically sqrtx=+-sqrtx

@Ostup_Burtik 4 месяца назад

@joshuahillerup4290 3 года назад

And this is why I cringe slightly every time you (or anyone else) goes from the square root of a value to that value to a one half power without addressing that they're slightly different.

@yarakharam5343 3 года назад

I dont get what you're saying, how are they different?

@joshuahillerup4290 3 года назад

@@yarakharam5343 x^2 and x^(1/2) are inverses of each other. The square root of x is a function that takes the principal root of x^(1/2)

@shashankambone6920 3 года назад

Pretty sure that the x^(1/2) is not how we represent the multivalued root of x.... i mean that x^(1/2) = sqrt(x)... same domain, same range, same function.

@joshuahillerup4290 3 года назад

@@shashankambone6920 not what I was taught. The radix is a function, a non-integer exponent is not

@shashankambone6920 3 года назад

@@joshuahillerup4290 maybe we have different conventions...