I AM CONCURRENTLY WATCHING ZUNDAMONS THEOREM IN ENGLISH AND JP TO LEARN TWICE AS FAST. I CAN FEEL MY BRAIN EXPAND AND STRETCH OUT TO THE VERY VESTIGES OF MY SKULL. ABSTRACTED NESTED CESARO MEANS HAVE LED TO ME TO ENLIGHTENMENT. I MUST GIVE YOU MY THANKS, ZUNDAMON.
as a mathematician i dislike the usage of the =... but the video is very good! a great intro to this topic!!! its also important to talk about the differences between this summation and the "normal" summation though... would appreciate a continuation on this so to defuse confusion in the minds of the less familiar with the topic (as this topic leads to the 1+2+3+...=-1/12 topic which NumberFile did years ago in a fashion that made math communicators struggle greatly as NumberFile did a disservice to the topic, rigorously speaking, while doing too good of a job at making the topic easy to digest for the average viewer). anyways liked the vid! looking forward for the next one no matter what the topic is! (i have a suggestion of making a vid about how complexity can arise from simple rules, like the Mandelbrot set for example, a really captivating idea!) much love
I discovered a method related to the pascals triangle in physics class :) If you just do some playing around with pascals triangle you will quickly notice that the sum of the numbers in the nth row is always 2^n (It generally doubles when you go down a row) Another thing you can do is expand the triangle upwards: 01-1+1-1+1-1+1-1 (-1st row Row sum=2^(-1) 1 0 0 0 0 0 0 0 (0th row Row sum = 2^0 11 (1st row Row sum = 2^1 121 (2nd row Row sum = 2^2 1331 (3rd row Row sum = 2^3 I think it is better if you sketch this out on some paper but yeah. The -1st row is our 1-1+1-1+1-1+1-1....... infinite sum and the row sum is equal to 1/2 We can continue this idea: the next row with a row sum of 2^(-2) will be the 1-2+3-4+5... series. The next row would be the oscillating sum of the triangular numbers 1-3+6-10+15... The next row is the oscillating sum of the lesser known tetrahedron numbers 1-4+10-20 As we go up, we will see the oscillating sum of 4d tetrahedron numbers, 5d tetrahedron numbers... This will quickly become boring. What if we want to calculate the sum of oscillating fibonacci numbers? Lets start with 0+0+0+0+1-1+2-3+5-8... = x and use the rules of pascals triangle 0+0+0+0+1-1+2-3+5-8... = x 0 0 0 1 0 1 -1 2 -3 = 2x since the row sum always doubles when we go down a row If we look closely we can see that the second row is also just 1 + the 1st row or 1+x 2x=Second row=1+x 2x=1+x => x=1 So the row sum of 1-1+1-3+5-8... is 1 Using similar methods, we can calculate the sum of the alternating square numbers 1-4+9-16... (i got 0) or the sum of alternating exponential numbers 1-2+4-8+16 (i got 1/3). Its really fun to get these unexpected results to these seemingly impossible to evaluate series. I encourage all of you to evaluate some of these alternating series. maybe even make up your own sequence and calculate its alternating sum. And i will also leave a quick exercise for the reader :P Evaluate the infinite product 2/2*2/2*2/2*2/2... using a variation of pascals triangle
if you find a rigorous way to define summation in a way that lets you show this connection your paper will be one of the coolest I've read ever!!! im really looking forward for your contribution to the world for recreational maths and who knows, maybe applied maths as well!!!
This is my favorite math channel ❤ I like how it explains math concepts simply and i also like Zundamon and Metan, one a curious student and the other an understanding and supportive teacher
Really wish I had something like this that started with algebra and worked its way up. I have a nephew who used youtube to self teach himself multiplication by the age of 3. He kind of stalled out there though. Conventional lessons bore him and he quickly loses interest and forgets and youtube videos suddenly become much more serious and a lot less fun after multiplication so he doesn'twatch them. This strikes a good balance of cute, easy to understand, and fun, but the topics are far to advanced for a kid trying to learn algebra.
A funny way to solve it is to say that it's the solution of x²-x(both have the solution 0 and 1) and lets just remove the delta term(so we can remove the variation) and we will get -(-1)/(2*1)=1/2
thank you for bestowing thy knowledge upon me. with this power i am henceforth going on a journey to calculate 1+2+3+4+5+... wish me luck with thine divine grace. (sorry for bad english)
For the 1 - 1 + 1 - 1... Series, i prefer to use the definition of geometric sum with a limit. If you were to plug in r=-1 and a=1, you will get: lim x->inf 1((-1)^x -1) / -1-1 (-1)^inf undefined, so whole expression is undefined. Cesaro sum is exciting, but i would like to apply it somewhere else :l
Limits are not the same thing as actual values of sums. Even *if* they were (which they aren't always), where is the justification for using the Cesaro or Abel approaches here? Metan did a whole lot of hand waving this video. So, sadly, I was somewhat disappointed this time. This was a good introduction. But, I do hope you go into a whole lot more detail in the future. PS: Oh, man another commenter made me notice how funny your video title is (again if we accept limits as being sums).
The definition of a partial sum is arbitrary. Really some mathematicians just declared that a partial is like this and that taking the limit of a partial sum is equal to the infinite sum of an infinite series. There is no proof for it. We just assume axiomaticaly that it is true. But since it is an axiom you can replace it with a different axiom. That is why there are alternate definitions of a sum of an infinite series. Just like there are alternate fifth postulates that results into non-Euclidean geometry.
No it doesnt First we simplify 1/(1-x) into (1-x)^-1 Then using the chain rule, we differntiate it into -1 * (1-x)^-2 * -1 Both -1 terms cancel oit and thus we are left with (1-x)^-2 , hence 1/(1-x)^2
Zundamon is replacing the Indian TH-camrs who got me through my college courses all those years ago.
😂 it cant as she give more abstract ones not basics.
I AM CONCURRENTLY WATCHING ZUNDAMONS THEOREM IN ENGLISH AND JP TO LEARN TWICE AS FAST. I CAN FEEL MY BRAIN EXPAND AND STRETCH OUT TO THE VERY VESTIGES OF MY SKULL. ABSTRACTED NESTED CESARO MEANS HAVE LED TO ME TO ENLIGHTENMENT. I MUST GIVE YOU MY THANKS, ZUNDAMON.
wut
oh no infinite brain series
@@AmeMori35¿How could we make this series correspond to a single value?
@@Bombito_ By watching them all.
Bro is Vsauce 💀
At the fringes of this video, I hear an evil voice cackling... it is saying something to me... it is whispering....... -1/12........
I thought I was the only one who heard this voice. But it seems I'm not alone...
Ramanujan...
Did anyone say the inverse of the harmonic series?
timestamp?
@farhanrejwan it's not in the video, it's in his head
I love how these concepts are explained properly and not the way Numberphile did it with -1/12. Love your approach to teaching a lot, good job!
Ah the infamous numberphile video. Really gotta appreciate how it's become a benchmark since it was quite badly explained lol
You're the best math teacher I never had so far, big thanks
This method of teaching works mysteriously amazing
Zundamon delivered more for us, all hail Zundamon’s Theorem
Why are these vids so captivating to watch! Amazingly instructive and interactive
Well, this is almost a simulation of an interaction between a good teacher and a listening student. That makes it a bit easier to understand
as a mathematician i dislike the usage of the =... but the video is very good! a great intro to this topic!!! its also important to talk about the differences between this summation and the "normal" summation though... would appreciate a continuation on this so to defuse confusion in the minds of the less familiar with the topic (as this topic leads to the 1+2+3+...=-1/12 topic which NumberFile did years ago in a fashion that made math communicators struggle greatly as NumberFile did a disservice to the topic, rigorously speaking, while doing too good of a job at making the topic easy to digest for the average viewer).
anyways liked the vid! looking forward for the next one no matter what the topic is! (i have a suggestion of making a vid about how complexity can arise from simple rules, like the Mandelbrot set for example, a really captivating idea!) much love
I appreciate this, especially the proper explanation of Cn. Far too many channels state the Cesaro Mean as the limit of the sequence, which it _isnt_
This video reawakened my -1/12 phobia (Imma name it Negaunciaphobia (uncia means 1/12 in Latin))
I discovered a method related to the pascals triangle in physics class :)
If you just do some playing around with pascals triangle you will quickly notice that the sum of the numbers in the nth row is always 2^n (It generally doubles when you go down a row)
Another thing you can do is expand the triangle upwards:
01-1+1-1+1-1+1-1 (-1st row Row sum=2^(-1)
1 0 0 0 0 0 0 0 (0th row Row sum = 2^0
11 (1st row Row sum = 2^1
121 (2nd row Row sum = 2^2
1331 (3rd row Row sum = 2^3
I think it is better if you sketch this out on some paper but yeah. The -1st row is our 1-1+1-1+1-1+1-1....... infinite sum and the row sum is equal to 1/2
We can continue this idea: the next row with a row sum of 2^(-2) will be the 1-2+3-4+5... series.
The next row would be the oscillating sum of the triangular numbers 1-3+6-10+15...
The next row is the oscillating sum of the lesser known tetrahedron numbers 1-4+10-20
As we go up, we will see the oscillating sum of 4d tetrahedron numbers, 5d tetrahedron numbers...
This will quickly become boring.
What if we want to calculate the sum of oscillating fibonacci numbers?
Lets start with 0+0+0+0+1-1+2-3+5-8... = x and use the rules of pascals triangle
0+0+0+0+1-1+2-3+5-8... = x
0 0 0 1 0 1 -1 2 -3 = 2x since the row sum always doubles when we go down a row
If we look closely we can see that the second row is also just 1 + the 1st row or 1+x
2x=Second row=1+x 2x=1+x => x=1
So the row sum of 1-1+1-3+5-8... is 1
Using similar methods, we can calculate the sum of the alternating square numbers 1-4+9-16... (i got 0) or the sum of alternating exponential numbers 1-2+4-8+16 (i got 1/3).
Its really fun to get these unexpected results to these seemingly impossible to evaluate series. I encourage all of you to evaluate some of these alternating series. maybe even make up your own sequence and calculate its alternating sum.
And i will also leave a quick exercise for the reader :P
Evaluate the infinite product 2/2*2/2*2/2*2/2... using a variation of pascals triangle
if you find a rigorous way to define summation in a way that lets you show this connection your paper will be one of the coolest I've read ever!!! im really looking forward for your contribution to the world for recreational maths and who knows, maybe applied maths as well!!!
This is my favorite math channel ❤
I like how it explains math concepts simply and i also like Zundamon and Metan, one a curious student and the other an understanding and supportive teacher
I literally got an exam about this in about 2 weeks
Thank you so much zundamon!
Can't believe you don't touch the "sum of all positive integers" topic
I struggled with this problem for a very long time, I didn't know the cesáro sum. Thank you Zundamon
Haven't finished video, I'm hoping it's the infamous -1/12 video
Edit: it's not, but its still a good video
The infamous Ramanujan Sum...
yet another quality upload from zundamons theorem
Really wish I had something like this that started with algebra and worked its way up. I have a nephew who used youtube to self teach himself multiplication by the age of 3. He kind of stalled out there though. Conventional lessons bore him and he quickly loses interest and forgets and youtube videos suddenly become much more serious and a lot less fun after multiplication so he doesn'twatch them. This strikes a good balance of cute, easy to understand, and fun, but the topics are far to advanced for a kid trying to learn algebra.
I just found out there’s an English version of the channel, nice!!
your channel is so cute and informative :) keep it up!
another amazing Zundamon post 🙏
Hmmm... I wonder what's that castle in the background?
평소에 이게 궁금했어요. 정말 고마워요❤
A funny way to solve it is to say that it's the solution of x²-x(both have the solution 0 and 1) and lets just remove the delta term(so we can remove the variation) and we will get -(-1)/(2*1)=1/2
thank you for bestowing thy knowledge upon me.
with this power i am henceforth going on a journey to calculate 1+2+3+4+5+...
wish me luck with thine divine grace.
(sorry for bad english)
your videos are amazing!
Hey everyone stop what your doing, new Zundamon's Theorem video is just dropped.
Thank you so much for the videos!)
The first one:
x=1-x
2x=1
x=1/2
The second one:
Yeah... I don't see any patterns that can be said with simple subsitution...
For the 1 - 1 + 1 - 1... Series, i prefer to use the definition of geometric sum with a limit. If you were to plug in r=-1 and a=1, you will get:
lim x->inf 1((-1)^x -1) / -1-1
(-1)^inf undefined, so whole expression is undefined.
Cesaro sum is exciting, but i would like to apply it somewhere else :l
I love the way they both pronounce cesàro in
Is there a generalization of this to other types of averages and means not just the arithmetic one?
Would really like your take on -1/12 thingy, great video btw
9:10
Metan!! How could you do this to us 😭😭😢😢
another amazing vid
for some reason i can understand math way better this way. Good video
1 - 1 + 1 is -1
because of PEMDAS (Parentheses Exponents Multiplication Division Addition Subtraction)
Can you explain ramanujan series next and other types of similar patterns? Thank you.
Yo man, hete we go again, awesome feeling
11:36 역은 성립하지 않는 반례가 있나요?
9:32 "anyway we got an answer" 😂😂😂😂😂😂😂😂😂😂😂😂
sensory fruit videos + advanced math = zundamons theorem
if you notice, the audio is more human the more videos they post!
If you release merch(eg. t-shirt), I will buy it 😚
Cesàro: an Italian name pronounced by a Japanese TTS imitating English... Somehow not that terribly done.
Limits are not the same thing as actual values of sums. Even *if* they were (which they aren't always), where is the justification for using the Cesaro or Abel approaches here? Metan did a whole lot of hand waving this video. So, sadly, I was somewhat disappointed this time. This was a good introduction. But, I do hope you go into a whole lot more detail in the future. PS: Oh, man another commenter made me notice how funny your video title is (again if we accept limits as being sums).
The definition of a partial sum is arbitrary. Really some mathematicians just declared that a partial is like this and that taking the limit of a partial sum is equal to the infinite sum of an infinite series. There is no proof for it. We just assume axiomaticaly that it is true. But since it is an axiom you can replace it with a different axiom. That is why there are alternate definitions of a sum of an infinite series. Just like there are alternate fifth postulates that results into non-Euclidean geometry.
wake up babe new zundamons theorem dropped
Please make a video about the graphic of factorial function and why it looks so strange
P.s. to say correctly make a video about gamma function. Because factorial is discrete func
Zundamon! My headphones suck....I need math to help fix them!
What is name of other(pink) character??
Props to creator! video was amazing and informative❤
She's Metan😆
When group theory 🗣️🗣️🗣️
>starts channel a month ago
>posts a very well-edited video about a math topic
>gains thousands of subs
>refuses to elaborate
It's because the Japanese channel already had lots of English-speaking fans who subbed quickly when this new English channel was made
thanks for this video!!1!!1!1!!
I love zundamon and metan❤
I love you zundamon
Zundamon is cute
Zundamon...IN ENGLISH?!
Interesting that the music seems to always be in triple metre
9:11 Ah no, no me van a aplicar esa
honey wake up new zundamons theorem
Wait, is the video title a pun? Lmao
please do imo p1/p4s
Ahh yes Vtuber teaches math.
10:52 shouldn’t dat be negative
No it doesnt
First we simplify 1/(1-x) into (1-x)^-1
Then using the chain rule, we differntiate it into -1 * (1-x)^-2 * -1
Both -1 terms cancel oit and thus we are left with (1-x)^-2 , hence 1/(1-x)^2
Hi!!
im early (i shouldnt be flexing this)
Elin music
Let S = 1-1+1-1+1-1+ …
S = 1-(1-1+1-1+1-1+ …)
S = 1-S
2S = 1
S = ½
You cannot rearrange a divergent series.
@ then why does it work
@@prod_EYES It does not always work.
For example
S= 1-1+1-1+1-1+1...
S= 1-(1-1+1-1+1-1...)
S= 1-(1-(1-1+1-1+1))
S= 1-(1-S)
S+(1-S)=1
S-S+1=1
1=1