Bedankt man! Duidelijke uitleg en een antwoord op mijn vraag. Ik ben blij om de honderdste like te kunnen geven. 👍

Wow thank you so much! I had this exact problem on my exam and could not figure it out for the life of me. Thank you this video really helped me out 👍

Partial Converse: If a and b are greater 0, and if there exist integers x and y such that ax + by = 1 then gcd(a,b) = 1 Prf: Let d = gcd(a,b) If 1 = bx + ay then 1 = d( b/d)x + d ( a/d)y or 1 = d( xb/d + ay/d) The quantity in brackets is an integer for b/d and a/d are integer; this tells us that d|1 or d=1 so that gcd(a,b) = 1

Very helpful and well explained!

Hi, may I know how to know when to stop reiterating in numerical methods if I am also asked to solve for percentage difference?

How do I know if it is analytic or not? Please explain in simple words.

thanks

ty so much ,but i wonder why im(a) is not (2 0 -1)T, (4 0 2)T, (-1 0 3)T . since those three vectors are linearly independent

Where did the I (imaginary part) go when you raised it to the square root??

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ive watched a couple videos on these and it clicked for me finally from this video, thank you so much! i subbed :)

Life saver. Hope everything is all well for you and thank you for the tremendous help!

Never explained where the 2x came from

wow its nice study

HOLY $H1T IS THAT RAMIEL-

Thank you, surprising no one said that to you in 4 years!

why 1/N+1 and -1/N+2 approaches to 0?

i appreciate it

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Good boy that’s what I like

Hi, do we actually end up getting the same value for area element as if it wasn't actually rectangular, because you say that we have to pretend that it's rectangular.

Great video :)

thank you so much...

Thank you sir

thanks for such clarity

You are very underrated!! Very helpful thank you

beautifully and simply explained!

I couldn't understand Theorem 1.6 from Apostol's book, I believe this is a lot more clear. Not sure why Apostol chose such a convoluted way of proving the theorem, only way I could think of is that he assumed reader/student doesn't know two assisting theorems on the video that would help advance further more efficiently.

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Easy to follow derivation by first principles, well described, well animated. No mucking around. Solid video.

thanks

Great and neat proof! I learned a lot, specially regarding the well-ordering principle!

thanks 😃

Holy hell this was insanely helpful. Thanks a ton sir

Thanks a lot good sir!

i like how this guy writes everything in logical statements

Can i not just say that a_n converges to a, so the choice of Epsilon in N2, can be |b_n - b| < 0.5E/|a|?

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one video and I understand everything. you are a GOAT. (greatest of all time)

Where did all the numbers go

The best explanation so far ❤

merci

thank you for posting this! I've been testing root-finding methods in geogebra. do you know of a way to implement something like secant method where you are looking at the previous two points? generating a table is possibly straightforward, not sure if it is possible in a script or Iteration function.

There we go, that’s fantastic thank you.

Thank you, this was immensely helpful for reinforcing my idea of, what it means to prove something by induction.

thaaank you that was helpful and super clear!!

🎉🎉🎉🎉thanks

thank you very much for the video. but please what happened to the "B" in the case 3? i thought it will be the coefficient of the sine function

isn't it that when gcd(a,b)|(ax+by) then gcd(a,b) = ax + by already because of well ordering principle and the gcd itself let's say when gcd(4,6) = 2 then we have 2|ax+by hence ax + by must be equal to 2.