This is an interesting derivation of Cauchy`s Schwarz inequality. However, an alternative derivation is to use vector identities such as A*B=|A|*|B|*cos(θ). What is cos(θ) in higher dimensions?!
@gingerderidder8665Күн бұрын
Please make more graph theory videos. The production value on this video matches 3B1B. Great stuff!
@vamruleКүн бұрын
Where's the +c
@gdmathguyКүн бұрын
great, now do a visual proof for all 1/n such that it sums to 1/(n-1)
@AZALI000132 күн бұрын
my eyes
@aspalt83 күн бұрын
Excuse me wtf
@jacksonherron28897 күн бұрын
Thanks for the educational video!! :)
@denyraw9 күн бұрын
I paused the video and solved it, then I was like "what is he cooking?" √(1+2√(1+3√(1+4√...))) Has the structure f(x) = √(1+x√...) where x is increasing with every repetition In order to have x increase with every repetition, I replaced the √... with f(x+1) f(x) = √(1+x•f(x+1)) The √ can be removed by squaring both sides, since they are always positive. f(x)² = 1 + x•f(x+1) This looks like f(x) could be a polynomial. I first tried to find the degree of f(x), if it were a polynomial. The degree of f(x) is a. Then the degree of f(x)² is 2a and the degree of 1+x•f(x+1) is a+1. We get: 2a = a+1 a = 1 Thus f(x) is linear. f(x) = mx + n (mx + n)² = 1 + x•(m(x+1) + n) m²x² + 2mnx + n² = mx² + (m+n)x + 1 The coefficients of the individual terms must be equal m² = m 2mn = m + n n² = 1 The only solution is m=1 n=1 f(x) = mx + n = x + 1 Since f(x) = √(1 + x√...) = √(1 + 2√...) We finally get: √(1 + 2√...) = f(2) = 2 + 1 = 3
@neitoxotien225810 күн бұрын
How about asking "Why is this card *Not* Banned???"
@RandomisedName11 күн бұрын
Man, some do it in 3 videos, what you did is a freaking speedrun😂
@Iamfafafel12 күн бұрын
eventually, i really want to see someone make a comparison between spectral theory on closed manifolds and on compact graphs. there are too many similarities too be a coincidence. as a baby example, theorem one also holds on manifolds. as for the video, i think the strongest block is the one starting at 9:10. the introduction was too fluffy, and the end was too unfocused. too much fluff risks alienating the audience. it would've been better to split it into different videos. nonetheless, thank you for making a video on a very interesting subject
@stochasticks12 күн бұрын
What in the fuck did I just witness
@stochasticks12 күн бұрын
I somehow have liked and subscribed
@40.vedantdubey8c612 күн бұрын
This is just sum of infinite GP
@user-lf3rz4ou5b13 күн бұрын
I really like it. some confusing parts after 21:20.(Fiedler Vector) could you please discuss about the below important lemmas as well: Perron-Frobenius Theorem Rayleigh Quotient Courant-Fischer Theorem Cheeger’s Inequality Spectral Radius Algebraic Connectivity (Fiedler’s Theorem) Weyl’s Inequality Eigenvalue Interlacing Lovász Local Lemma
@goofball-zo2xf13 күн бұрын
I pray for your misfortune
@doctordoctor129913 күн бұрын
No, it actually goes infinitely close to 1, 1/2, 1/3.
@Scotty-vs4lf13 күн бұрын
no, it goes to 1, 1/2 and 1/3
@savros-yb4zf11 күн бұрын
Such a distinction does not need to be made as we had already assumed the series continues infinitely.
@ferlywahyu34213 күн бұрын
This man like godel and hypasus 😂
@sushileaderyt195714 күн бұрын
It’s not a perfect square
@Near_Void14 күн бұрын
The sum of all fractions 1/(n^x) where x is every number and n is an interger is equal to 1/n-1
@palaashtrivedi492014 күн бұрын
f(x) = 0?😂 , 0:05
@user-ps7ij9bg4w15 күн бұрын
4pi radius squared
@Walkie-Talkie-zz9ck15 күн бұрын
😂😂😂
@kyanilcauli900216 күн бұрын
As a Math major, the feelings this video generates exactly how I felt when I was attending a class of Mathematical Methods in Physics for a Minor. We were taught many methods of solving Differential Equations, and also, Complex Analysis - in which I struggled to gasp a single thing as most explanations were as non-sensical as this. I wish I was joking. My heart finally felt at ease when I revisited all this concepts later on in courses meant for Math Majors, under completely different instructions for each discipline. Edit: Note:- for the people who argue this is fine if you view integral as a linear differential operator from a banach space to another (space of differentiable maps to space of continuous maps) and I do agree, the "so it must be 1" is still jack. I understand the video is a joke, and while I am still giggling at the joke, I certainly won't assert some statement for which is incomplete. Functional Analysis isn't trivial. The people who properly explained it in the comments have my gratitude though, as they simply didn't just say "Functional Analysis" and called it a day.
@neuralwarp17 күн бұрын
Create a sparrow ?
@connordovah793317 күн бұрын
Ok, I get this... What's the next bit? How is this useful to developing mathematical understandings? Is there a takeaway beyons just the aum to infinities?
@RandotMS17 күн бұрын
It's about the spin Johnny.
@denisday1417 күн бұрын
Infinite 1/5 is 1/4 of the area?
@mosescheung579414 күн бұрын
yeeeeeeep
@user-qp6il7wc5n17 күн бұрын
Great visualisation!
@tachytwo253417 күн бұрын
when you blink in class😂
@jorgelombardi16918 күн бұрын
¿Always a Graph matrix are symetric? indiferently of the type of graph?
@ron-math18 күн бұрын
The graph has to be unidirectional in order for the matrices to be symmetric.
@bsbx19 күн бұрын
f(x) = B f'(x) = A f''(x) = C
@killianobrien200719 күн бұрын
The problem is you cant say "2x or 0.5x" bc in each case the x is different and shouldnt be represented with the same thing
@nirorit19 күн бұрын
B’ = A A’ = C
@sodiumfluoridel19 күн бұрын
Wait according to this you could divide by e^x at the start and get that integral of one equals one
@nebularwinter20 күн бұрын
Say you remove 5 dollars from both envelopes. Then your odds get better: one envelope has 0 dollars and the other one 5 dollars, and by the same computation with "expected returns", the expected return of switching is INFINITY.
@EdKolis19 күн бұрын
What if you took $8 out of each, leaving negative money inside the one that had $5? Then there would be negative incentive to switch no matter which you pick!
@driksarkar667519 күн бұрын
@@EdKolisThat is, you would be incentivized to keep your current envelope.
@shayomarcopion20 күн бұрын
This is like that one meme where you get to choose if you want to swallow the red pill or blue pill but both choices are balanced. It's a 50/50, what do you expect? Even if you think about changing or staying in the answer, we wouldn't know which is which. 50/50 will always be like that, and will *BE* like that. The law of 50/50 can't be broken.
@asemalawiHb20 күн бұрын
I love it
@GeoffryGifari20 күн бұрын
wonder if ramanujan found the solution or the original nested radical first
@nokhinsiu721020 күн бұрын
Bro proved intergral = 1 and 1/0= 1+1+1²...
@alexanderlevakin900120 күн бұрын
I like the part where you substitute f(x) for x+2n+a despite f(x) is x+n+a by definition.
@CleverMathematics20 күн бұрын
Do you mean the part where he substituted f(x+n) for x+2n+a?
@nebularwinter20 күн бұрын
I liked the part where you introduce "a" and then 4 steps later, you just put "a=0"
@stone732722 күн бұрын
This is so funny. I busted out laughing more than once lol
Пікірлер
This is an interesting derivation of Cauchy`s Schwarz inequality. However, an alternative derivation is to use vector identities such as A*B=|A|*|B|*cos(θ). What is cos(θ) in higher dimensions?!
Please make more graph theory videos. The production value on this video matches 3B1B. Great stuff!
Where's the +c
great, now do a visual proof for all 1/n such that it sums to 1/(n-1)
my eyes
Excuse me wtf
Thanks for the educational video!! :)
I paused the video and solved it, then I was like "what is he cooking?" √(1+2√(1+3√(1+4√...))) Has the structure f(x) = √(1+x√...) where x is increasing with every repetition In order to have x increase with every repetition, I replaced the √... with f(x+1) f(x) = √(1+x•f(x+1)) The √ can be removed by squaring both sides, since they are always positive. f(x)² = 1 + x•f(x+1) This looks like f(x) could be a polynomial. I first tried to find the degree of f(x), if it were a polynomial. The degree of f(x) is a. Then the degree of f(x)² is 2a and the degree of 1+x•f(x+1) is a+1. We get: 2a = a+1 a = 1 Thus f(x) is linear. f(x) = mx + n (mx + n)² = 1 + x•(m(x+1) + n) m²x² + 2mnx + n² = mx² + (m+n)x + 1 The coefficients of the individual terms must be equal m² = m 2mn = m + n n² = 1 The only solution is m=1 n=1 f(x) = mx + n = x + 1 Since f(x) = √(1 + x√...) = √(1 + 2√...) We finally get: √(1 + 2√...) = f(2) = 2 + 1 = 3
How about asking "Why is this card *Not* Banned???"
Man, some do it in 3 videos, what you did is a freaking speedrun😂
eventually, i really want to see someone make a comparison between spectral theory on closed manifolds and on compact graphs. there are too many similarities too be a coincidence. as a baby example, theorem one also holds on manifolds. as for the video, i think the strongest block is the one starting at 9:10. the introduction was too fluffy, and the end was too unfocused. too much fluff risks alienating the audience. it would've been better to split it into different videos. nonetheless, thank you for making a video on a very interesting subject
What in the fuck did I just witness
I somehow have liked and subscribed
This is just sum of infinite GP
I really like it. some confusing parts after 21:20.(Fiedler Vector) could you please discuss about the below important lemmas as well: Perron-Frobenius Theorem Rayleigh Quotient Courant-Fischer Theorem Cheeger’s Inequality Spectral Radius Algebraic Connectivity (Fiedler’s Theorem) Weyl’s Inequality Eigenvalue Interlacing Lovász Local Lemma
I pray for your misfortune
No, it actually goes infinitely close to 1, 1/2, 1/3.
no, it goes to 1, 1/2 and 1/3
Such a distinction does not need to be made as we had already assumed the series continues infinitely.
This man like godel and hypasus 😂
It’s not a perfect square
The sum of all fractions 1/(n^x) where x is every number and n is an interger is equal to 1/n-1
f(x) = 0?😂 , 0:05
4pi radius squared
😂😂😂
As a Math major, the feelings this video generates exactly how I felt when I was attending a class of Mathematical Methods in Physics for a Minor. We were taught many methods of solving Differential Equations, and also, Complex Analysis - in which I struggled to gasp a single thing as most explanations were as non-sensical as this. I wish I was joking. My heart finally felt at ease when I revisited all this concepts later on in courses meant for Math Majors, under completely different instructions for each discipline. Edit: Note:- for the people who argue this is fine if you view integral as a linear differential operator from a banach space to another (space of differentiable maps to space of continuous maps) and I do agree, the "so it must be 1" is still jack. I understand the video is a joke, and while I am still giggling at the joke, I certainly won't assert some statement for which is incomplete. Functional Analysis isn't trivial. The people who properly explained it in the comments have my gratitude though, as they simply didn't just say "Functional Analysis" and called it a day.
Create a sparrow ?
Ok, I get this... What's the next bit? How is this useful to developing mathematical understandings? Is there a takeaway beyons just the aum to infinities?
It's about the spin Johnny.
Infinite 1/5 is 1/4 of the area?
yeeeeeeep
Great visualisation!
when you blink in class😂
¿Always a Graph matrix are symetric? indiferently of the type of graph?
The graph has to be unidirectional in order for the matrices to be symmetric.
f(x) = B f'(x) = A f''(x) = C
The problem is you cant say "2x or 0.5x" bc in each case the x is different and shouldnt be represented with the same thing
B’ = A A’ = C
Wait according to this you could divide by e^x at the start and get that integral of one equals one
Say you remove 5 dollars from both envelopes. Then your odds get better: one envelope has 0 dollars and the other one 5 dollars, and by the same computation with "expected returns", the expected return of switching is INFINITY.
What if you took $8 out of each, leaving negative money inside the one that had $5? Then there would be negative incentive to switch no matter which you pick!
@@EdKolisThat is, you would be incentivized to keep your current envelope.
This is like that one meme where you get to choose if you want to swallow the red pill or blue pill but both choices are balanced. It's a 50/50, what do you expect? Even if you think about changing or staying in the answer, we wouldn't know which is which. 50/50 will always be like that, and will *BE* like that. The law of 50/50 can't be broken.
I love it
wonder if ramanujan found the solution or the original nested radical first
Bro proved intergral = 1 and 1/0= 1+1+1²...
I like the part where you substitute f(x) for x+2n+a despite f(x) is x+n+a by definition.
Do you mean the part where he substituted f(x+n) for x+2n+a?
I liked the part where you introduce "a" and then 4 steps later, you just put "a=0"
This is so funny. I busted out laughing more than once lol