Why it doesn't converge to 3?

  Рет қаралды 99,911

blackpenredpen

blackpenredpen

Күн бұрын

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 kzfaq.info...
Shop math t-shirts: teespring.com/stores/blackpen...
Support: / blackpenredpen
Follow: / blackpenredpen
blackpenredpen,
math for fun

Пікірлер: 164
@141Zero
@141Zero 4 жыл бұрын
The Lambert W function is a pathway to many abilities some consider to be unnatural.
@dihydrogenmonoxid1337
@dihydrogenmonoxid1337 3 жыл бұрын
But will it save padme?
@juandaviolin
@juandaviolin 3 жыл бұрын
¿що ти думал? From a certain death?
@That_One_Guy...
@That_One_Guy... 3 жыл бұрын
But can it express x as a function of y that's elementary ? 😏
@nol2521
@nol2521 Жыл бұрын
@@dihydrogenmonoxid1337 you will fall in love with the lambert w function instead of padme so that question is irrelevant
@andyiswonderful
@andyiswonderful 3 жыл бұрын
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
@blackpenredpen 3 жыл бұрын
Thank you : )
@leif1075
@leif1075 3 жыл бұрын
@@blackpenredpen Why didnt you tskenthe natural log of both sides at 1:26 first?
@leif1075
@leif1075 3 жыл бұрын
@@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
@ozzymandius666 3 жыл бұрын
@@blackpenredpen Perhaps one day show us a graph of y=W(x).
@shashankambone6920
@shashankambone6920 3 жыл бұрын
@@ozzymandius666 just look at the graph of x=y×e^y... that's the graph of y=W(x)....
@MuPrimeMath
@MuPrimeMath 4 жыл бұрын
Those graphs are really cool!
@bendaniels7346
@bendaniels7346 3 жыл бұрын
Love your vids :)
@sharepremium8614
@sharepremium8614 3 жыл бұрын
How is ur comment 3 years ago wtf ?
@angelheretic2190
@angelheretic2190 3 жыл бұрын
how's your comment 3 months ago?
@AshrafAli-qn3gb
@AshrafAli-qn3gb 3 жыл бұрын
😱😱😱are you Gost
@bendaniels7346
@bendaniels7346 3 жыл бұрын
Wait yo what
@juandaviolin
@juandaviolin 3 жыл бұрын
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
@shreyan1362 3 жыл бұрын
Thanks ,,, i was shocked
@balaramkrishnahanumanthu5869
@balaramkrishnahanumanthu5869 4 жыл бұрын
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
@Prxwler 3 жыл бұрын
4:43 easy, k = w
@GianniCampanale
@GianniCampanale 3 жыл бұрын
🤦‍♂️
@quirtt
@quirtt 3 жыл бұрын
XD
@maskedman8368
@maskedman8368 3 жыл бұрын
🤦‍♂️🤦‍♂️🤦‍♂️
@siddharthabhattacharya3787
@siddharthabhattacharya3787 3 жыл бұрын
@@quirtt bhai tu idhar?
@shreyan1362
@shreyan1362 3 жыл бұрын
@@quirtt har jagah se padhte ho kya xd
@leickrobinson5186
@leickrobinson5186 3 жыл бұрын
That was a brilliant, beautiful explanation. Thank you!
@blackpenredpen
@blackpenredpen 3 жыл бұрын
Thanks!
@oskarkrogsgard3014
@oskarkrogsgard3014 3 жыл бұрын
@@AstroB7 what is going on....?
@frozenmoon998
@frozenmoon998 3 жыл бұрын
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
@xandersafrunek2151 3 жыл бұрын
When you said "power tower," it made me really happy.
@nou3227
@nou3227 3 жыл бұрын
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
@revoltoff 3 жыл бұрын
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
@marcusdecarvalho1354 3 жыл бұрын
Unbelievable! Extraordinary! Marvelous!
@soulsilencer1864
@soulsilencer1864 3 жыл бұрын
Hi, love your videos, can you take the integral from -2 to 2 sqrt(1-x^2) dx ?
@jibiteshsaha4392
@jibiteshsaha4392 3 жыл бұрын
Please someone explain me how does the fixed point convergence criteria come How does that interval come
@vaibhavm2916
@vaibhavm2916 3 жыл бұрын
Can you pls tell me which company markers do you use.they seem pretty easy to hold 2 in a hand and switch
@nafrost2787
@nafrost2787 3 жыл бұрын
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?
@ulanluhod9628
@ulanluhod9628 3 жыл бұрын
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
@LShadow77 3 жыл бұрын
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
@angelmendez-rivera351 4 жыл бұрын
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
@MK-rh4wx 3 жыл бұрын
i love how you explain it
@martinhimstedt5130
@martinhimstedt5130 Жыл бұрын
Excellent!
@benisjamin6583
@benisjamin6583 3 жыл бұрын
@blackpinredpin Looking fresh as always! Great video.
@omarfawaz1051
@omarfawaz1051 3 жыл бұрын
Beautiful... Thanks🌹
@jibiteshsaha4392
@jibiteshsaha4392 3 жыл бұрын
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
@efulmer8675 Жыл бұрын
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
@asharmasharma51 3 жыл бұрын
From India watching you nice concept loved it
@shruggzdastr8-facedclown
@shruggzdastr8-facedclown 2 жыл бұрын
Is there a number such that when applied to an infinite power tower it converges on pi?
@magicodabola10
@magicodabola10 4 жыл бұрын
Amazing!
@SuperYoonHo
@SuperYoonHo 2 жыл бұрын
very nice!
@rateeshk8175
@rateeshk8175 3 жыл бұрын
Is three (3) the only misbehaving number in these problems???
@gtziavelis
@gtziavelis 3 жыл бұрын
Well, well, well... excellent!
@peterruf1462
@peterruf1462 3 жыл бұрын
Why does the power tower oscillate if you chose x smaller than e^-e?
@rajmanitiwari5346
@rajmanitiwari5346 3 жыл бұрын
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
@glendagiron9685 3 жыл бұрын
Need your help. What is the answer here? x^x^x^x^... = 10
@georgeb8893
@georgeb8893 3 жыл бұрын
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
@shashankambone6920 3 жыл бұрын
So.. ln(100)/ln(x) = 3? Is that what we are trying to solve? Because that's trivial....
@xinpingdonohoe3978
@xinpingdonohoe3978 2 ай бұрын
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
@LUCATRON-hs8cj 3 жыл бұрын
Nice song at the end
@fsf471
@fsf471 3 жыл бұрын
Holy shit I was just thinking of this earlier did you read my mind?
@tomatrix7525
@tomatrix7525 3 жыл бұрын
Wow that function is cool
@gudmundurjonsson4357
@gudmundurjonsson4357 3 жыл бұрын
dont you also assume the the power tower of x can be written as 3 when replacing it, i.e. assuming it converges?
@mtaur4113
@mtaur4113 3 жыл бұрын
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
@shashankambone6920 3 жыл бұрын
Exactly. That's exactly the problem.
@beltin_time
@beltin_time 11 ай бұрын
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
@NekoAlosama 4 жыл бұрын
ooh
@shubhampradhan5348
@shubhampradhan5348 3 жыл бұрын
Sir please provide the PDFs of 100 integrals, 100 derivatives, 100 series... Humble request👍👍
@djvalentedochp
@djvalentedochp 4 жыл бұрын
Nice
@particleonazock2246
@particleonazock2246 3 жыл бұрын
You know you're dealing with advanced math when blackpenredpen doesn't summon the fish.
@oxygen2623
@oxygen2623 Жыл бұрын
1:00 Well, that escalated quickly
@joejavacavalier2001
@joejavacavalier2001 3 жыл бұрын
But how would you calculate W lambert values manually?
@savitsios
@savitsios 3 жыл бұрын
Same as the natural log, you basically can't Or with trial and error
@shashankambone6920
@shashankambone6920 3 жыл бұрын
@@savitsios i mean there are many ways to approximate....
@jibiteshsaha4392
@jibiteshsaha4392 3 жыл бұрын
I asked this in the previous video I want a proof for the fixed point convergence criteria
@i_saidmeow2469
@i_saidmeow2469 3 жыл бұрын
The chomper microphone!
@djttv
@djttv 3 жыл бұрын
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
@blackpenredpen 3 жыл бұрын
djttv It’s similar to this one kzfaq.info/get/bejne/l8yqZtdpt5mYomg.html
@djttv
@djttv 3 жыл бұрын
@@blackpenredpen I learned something new! Thank you
@Bobbius-il9rf
@Bobbius-il9rf 3 жыл бұрын
Brilliant XD
@basedblueboy8770
@basedblueboy8770 3 жыл бұрын
@ 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
@basedblueboy8770 3 жыл бұрын
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.
@meiwinspoi5080
@meiwinspoi5080 3 жыл бұрын
cool.
@willyou2199
@willyou2199 3 жыл бұрын
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.
@nafrost2787
@nafrost2787 3 жыл бұрын
This guys is really addicted to the W function.
@JSSTyger
@JSSTyger 3 жыл бұрын
I have a question. Does x^x^x equal x^(x^x) or (x^x)^x?
@Silvar55x
@Silvar55x 3 жыл бұрын
x^x^x = x^(x^x) always. You need parenthesis on (x^x)^x.
@JSSTyger
@JSSTyger 3 жыл бұрын
@@Silvar55x MicroSoft Excel says 3^3^3 = 19683
@Silvar55x
@Silvar55x 3 жыл бұрын
@@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
@evanlewis2349 4 жыл бұрын
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
@evanlewis2349 4 жыл бұрын
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
@angelmendez-rivera351 4 жыл бұрын
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.
@omshandilya8888
@omshandilya8888 3 жыл бұрын
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
@logicalproofs7276
@logicalproofs7276 3 жыл бұрын
Regular videos Woooooow
@justinlink1616
@justinlink1616 4 жыл бұрын
My head is going to expode.
@vaibhavm2916
@vaibhavm2916 3 жыл бұрын
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
@Dear999 3 жыл бұрын
Pendyala education and eentertainment 👍
@haval00
@haval00 3 жыл бұрын
How come some comments be from 1 month ago ??
@coc235
@coc235 3 жыл бұрын
This video was available by link
@blackpenredpen
@blackpenredpen 3 жыл бұрын
It was unlisted in my playlist
@haval00
@haval00 3 жыл бұрын
@@blackpenredpen Ok thank you , great video btw
@SoWe1
@SoWe1 3 жыл бұрын
ok I'm stupid why does -2 = sqrt(x) not have any solutions even in the complex plane? i*4?
@aeropoulpe7818
@aeropoulpe7818 3 жыл бұрын
sqrt(4*i) = 2 * sqrt(i) = 2 * ( sqrt(2)/2 + i*sqrt(2)/2 ) = sqrt(2) + i*sqrt(2)
@SoWe1
@SoWe1 3 жыл бұрын
@@aeropoulpe7818 sqrt(4*i) = 2 * sqrt(i) = 2*(-1) = -2
@aeropoulpe7818
@aeropoulpe7818 3 жыл бұрын
@@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
@SoWe1 3 жыл бұрын
@@aeropoulpe7818 rightrightright, yes but still, why does that equation not have any solutions?
@aeropoulpe7818
@aeropoulpe7818 3 жыл бұрын
@@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
@darshanvanjara6009 3 жыл бұрын
Integration of 1 /1+secx ..... PLEASE SUGGEST SIR......😔😔😔😔😔😔😔😔☹️
@darshanvanjara6009
@darshanvanjara6009 3 жыл бұрын
@3head individual done sir... THANKS a lot ..
@darshanvanjara6009
@darshanvanjara6009 3 жыл бұрын
@3head individual where are you from sir. Japan??
@ordinary1017
@ordinary1017 3 жыл бұрын
U're the best
@DeadJDona
@DeadJDona 3 жыл бұрын
6:22 how could complex numbers infinite power look?
@saisrirajnallam
@saisrirajnallam 3 жыл бұрын
Thank u maths teacher
@MeOKMeO
@MeOKMeO 3 жыл бұрын
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
@MeOKMeO 3 жыл бұрын
Downloaded a curve equation generator, between 1 and e
@shashankambone6920
@shashankambone6920 3 жыл бұрын
How many numbers? Infinite....
@aryanbhargav9705
@aryanbhargav9705 3 жыл бұрын
Now I am in future
@lupusofaquarius7434
@lupusofaquarius7434 4 жыл бұрын
Your pens surely hold infinite power!
@Silvar55x
@Silvar55x 3 жыл бұрын
@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
@GammaFZ 3 жыл бұрын
whatislambertwfunctionpleasemakeavideoonthatthanks
@TecknoVicking
@TecknoVicking 3 жыл бұрын
🔒
@swampman4204
@swampman4204 3 жыл бұрын
Hello bprp!!!!
@lawrencebermudez
@lawrencebermudez 4 жыл бұрын
e = 3
@satteshwaribharti9524
@satteshwaribharti9524 3 жыл бұрын
Hi.. I have a challange question for you.. 😂😂
@wallissoncoelho7451
@wallissoncoelho7451 3 жыл бұрын
How do you learned English?
@chinjunyuan1720
@chinjunyuan1720 3 жыл бұрын
3
@gordonchan4801
@gordonchan4801 3 жыл бұрын
henlo
@aryangupta904
@aryangupta904 3 жыл бұрын
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
@shashankambone6920 3 жыл бұрын
Wait what? You must be joking.....
@ipetmycats99
@ipetmycats99 3 жыл бұрын
how did I get here
@estelle_chenxing
@estelle_chenxing 3 жыл бұрын
hi
@jacobhall4655
@jacobhall4655 3 жыл бұрын
0:27 not according to physicists
@oscartroncoso2585
@oscartroncoso2585 3 жыл бұрын
First!
@ssdd1316
@ssdd1316 3 жыл бұрын
no
@purim_sakamoto
@purim_sakamoto 3 жыл бұрын
うーん むずかしかった
@purim_sakamoto
@purim_sakamoto 3 жыл бұрын
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
@gurkiratsingh7tha993 2 жыл бұрын
Technically sqrtx=+-sqrtx
@Ostup_Burtik
@Ostup_Burtik 4 ай бұрын
no
@joshuahillerup4290
@joshuahillerup4290 3 жыл бұрын
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
@yarakharam5343 3 жыл бұрын
I dont get what you're saying, how are they different?
@joshuahillerup4290
@joshuahillerup4290 3 жыл бұрын
@@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
@shashankambone6920 3 жыл бұрын
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
@joshuahillerup4290 3 жыл бұрын
@@shashankambone6920 not what I was taught. The radix is a function, a non-integer exponent is not
@shashankambone6920
@shashankambone6920 3 жыл бұрын
@@joshuahillerup4290 maybe we have different conventions...
@amiasam3354
@amiasam3354 3 жыл бұрын
Who came here from bprp fast
@gtafita6392
@gtafita6392 3 жыл бұрын
Nice
Solving 3 Weird Logarithm Equations
9:34
blackpenredpen
Рет қаралды 244 М.
Children deceived dad #comedy
00:19
yuzvikii_family
Рет қаралды 8 МЛН
ОДИН ДЕНЬ ИЗ ДЕТСТВА❤️ #shorts
00:59
BATEK_OFFICIAL
Рет қаралды 8 МЛН
are you tired of the a^b vs b^a questions?
12:42
blackpenredpen
Рет қаралды 923 М.
Solutions to x^y=y^x
13:09
blackpenredpen
Рет қаралды 1,1 МЛН
Solving An Insanely Hard Problem For High School Students
7:27
MindYourDecisions
Рет қаралды 3,4 МЛН
Solving x^i=1 vs i^x=1
13:35
blackpenredpen
Рет қаралды 142 М.
(infinity-infinity)^infinity
22:06
blackpenredpen
Рет қаралды 424 М.
Infinite Power Tower Equations Battle!
8:55
blackpenredpen
Рет қаралды 128 М.
Fear No Equation
8:46
BriTheMathGuy
Рет қаралды 121 М.
exact value of sin(3 degrees)
33:16
blackpenredpen
Рет қаралды 419 М.
Children deceived dad #comedy
00:19
yuzvikii_family
Рет қаралды 8 МЛН