Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem

[@fierydino9402]

Really exciting. Thank you!

[@connorfrankston5548]

In the boxed statement at 58:00, it should be: For all t in M and a in C, that |u(t)+a*L|

[@dingbo5590]

Good lecture. some comments about the lemma: for functional : X->C. F(x)=f(x)-if(ix) where f is a real functional.So ||f||=||F||.So we only need to prove the real part

[@SSNewberry]

Good use of Zorn's Lemma on expansion.

[@yeni_nick]

11:40 Can u explain how we conclude c is an element of E from the knowledge of FİNİTE collection of {v1,v2 ...vN} is linearly independent.Shouldn't be there an extra property like"closed under taking infinite union".(similar to the sigma-algebra has)

[@SSNewberry]

@@yeni_nick Principal of generosity because the extra principal is trivial.

[@yeni_nick]

@@SSNewberry i dont think it is trivial. Any FİNİTE sum of elements from Q is an element of Q but that's not the case for infinite sum if you think about the Cauchy which consist of Q but converging to an element of R.(not in Q)

[@yeni_nick]

I found the answer i guess.It stems from the definition of the Hamel basis and linear independence.If we was searching for "Schauder basis" my point would be an issue.

[@SSNewberry]

@@yeni_nick Thus it is trivial.

[@user-bk2fo7ny9s]

great lecture but... choice of letters in proofs is all over the place, for example don't use "u"/"v"for functionals when the space is V

[@LeoJi-j1e]

I'm a little bit confused about the last part of the lecture, why does the theorem hold if the imaginary part and the real part hold?

[@LeoJi-j1e]

like I think it's not obvious because by the triangular inequality it should be \sqrt{2} \Vert t-x\Vert right

[@sofiasofi2257]

It's making me dizzy when camera moves with the movement of professor

[@peasant12345]

so true. Why not focus on the blackborad.

[@freeeagle6074]

It seems the videos were made during the pandemic using an AI camera which automatically zooms on the person rather than the blackboard.

[@mark_tilltill6664]

Most of the space is wasted and the audio is not great either. It should zoom in his hand when he writes on the board. The zoom should should be so that the frame differencing is a maximum. This way the focus is exclusively on the professor.

[@TheIllerX]

Good lecture, just a few annoyances: The camera should focus on the text and not the lecturer. Also, personally I find all the "ah", "ehh" between the sentences extremely annoying. It disrupts my focus a lot, it sounds some sentence is coming but then there is just "ehh". Better not starting to speak until knowing what to say instead of trying to fill the void with these sounds.

[@sunritroykarmakar4406]

He s shockingly bad