Excellent video. Instead of spending an hour trying to read and understand the proof, you explain it super good in under 30 minutes. Thanks.
@MsDanni1234567894 жыл бұрын
I have been thinking about these things for months, finally I understand these concepts because of this video, you are so positive and make it more fun, well done!
@Leidl.Michael4 жыл бұрын
Zorns Lemma is such a powerful tool to prove things like this because you only have to prove something for totally ordered subsets of a partially ordered set, which makes things way easier. For an oral exam I had to learn the proof of the equivalence of the axiom of choice and Zorns Lemma, which didn't made me zornig at all. :D
@alvinlepik52655 жыл бұрын
It also turns out that every non-zero vector space having a basis is equivalent to the axiom of choice. The non-zero bit is important, because the zero vector doesn't constitute a linearly independent subset.
@nudelsuppe20903 жыл бұрын
Usually the span of an empty set is considered to be zero so you basically have an "empty basis" for that
@alvinlepik52653 жыл бұрын
@@nudelsuppe2090 good point. It's consistent, too. A finite linear combination over the empty set yields 0 vector.
@christianharriviktorreibol5521 Жыл бұрын
Is an union of sets in a chain not automatically in a chain and so automatically a member of the family of sets?
@MewPurPur3 жыл бұрын
This vid put me to sleep at first. Now I finally got it! Super helpful and thank you.
@cruzazul26094 жыл бұрын
Omg, I don't "dominate" the English and I learned more with you than with my professor who explained in my mother language SPANISH.
@ces-12003 жыл бұрын
Same :')
@highermathematics-bx4mi2 жыл бұрын
I am finding this theorem from 24 hours but I couldn't find such a video now alhamdulillah now I find your lecture and enjoy it 🥳🌹🥰 very amazing
@broccoloodle3 жыл бұрын
This guy's presentation is so charming :)
@HasXXXInCrocs4 жыл бұрын
So essentially for any infinite dimensional vector space, a combination of ideals of V is the basis of V? Is that what a chain is? Note that any principal ideal is independent because of the absorption property.
@dthhfjjjj4 жыл бұрын
I love this video, you explain it very clearly
@highermathematics-bx4mi2 жыл бұрын
🥳🥳🥳 very interesting manner of teaching
@ravitejassu5 жыл бұрын
Very beautifully explained
@schwarzeseis40315 жыл бұрын
Makes tons of sense. Gonna forget it again. Shall return.
@weinihao36325 жыл бұрын
Hi Dr. Peyam, thank you very much for the nice video. I found it a bit confusing that you described your sets with the term ring, since that is an algebraic structure by itself. In the beginning you shortlymention that the proof could also cover infinite dimensional vectorspaces, but in the end it is required that each member of the family is finite. Do you plan to add a follow up video to proof it for infinitely many dimensions as well?
@drpeyam5 жыл бұрын
But I proved it for infinite dimensions
@weinihao36325 жыл бұрын
@@drpeyam Oh, sorry, you are absolutely right! I missed your statement at 21:43. Thank you for the clarification!
@Handelsbilanzdefizit5 жыл бұрын
Does it make sense, to define a derivative like this? lim h-->0 (f(x+h)/f(x))^(1/h) = f*(x) As far as I figured out, you can easily calculate attenuation or "elementary" probabilities with that. It seems, the Inverse is some kind of Product Integral (infinity multiplying) If the chance I go to the party is 50%, and my friend visits the party 50%, then we meet us there 25%. But multiplying such probabilities infinity times, then you get some bellcurve e^-x² (for many cases)
@drpeyam5 жыл бұрын
Hehe, that’ll be part of another video to be posted sometime :)
@sandorszabo24705 жыл бұрын
I'm very missed this theorem, and now I could find this video. Soon start the next semester :-)
@dgrandlapinblanc5 жыл бұрын
I've listened and watched three times this video. Thanks.
@goatmatata27985 жыл бұрын
Hello Dr peyam, I have a humble request please create a video where u prove gauss's multiplication theorem for the gamma function, I have tried it a million times but just can't get it right, please 🙏 if you do it do it in a not so complicated way, thank you in advance, from 🇰🇪 kenya
@jonasdaverio93695 жыл бұрын
Zorn's lemma... That's reminding me some nightmares from when I was self-studying foundations of mathematics...
@lagduck22095 жыл бұрын
When he said it's equivalent to axiom of choice I've got strong flashbacks to when I was self-studying foundations of mathematics and lots of other topics bingeing wikipedia for hours, days, weeks and months; don't think I actually understood even 5% of what I studied, but it was fantastic trip through the beauty of maths, all of this interconnected world. And I can just barely follow this video nowadays, but I can so it's great. Also thanks for great interesting content and original ideas Dr
@jonasdaverio93695 жыл бұрын
I've always thought Zermelo's theorem doesn't make any sense (I mean, why would there be a well-order in R?) , axiom of choice isn't perticularly counterintuitive, and Zorn's lemma doesn't mean anything in term of intuition.
@russellsharpe2885 жыл бұрын
@@jonasdaverio9369: The wikipedia article on the Axiom of Choice contains the following quotation: "The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" - Jerry Bona"
@hungnguyen-fn8gm3 жыл бұрын
how did you do it can you share with me , thank you
@mrnarason5 жыл бұрын
Great explanation
@dhunt66185 жыл бұрын
Thanks for another great video. Sorry, but I can't resist mentioning the 2 related problems that Zorn couldn't prove - Zorn's dilemma... (sorry again, yes, it's an old pun)
@drpeyam5 жыл бұрын
Hahahahaha
@kgjplatform09872 жыл бұрын
I have some exercises...could you help me Dr. ?
@gdsfish32145 жыл бұрын
Our professor showed us in week two of first semester how zorn's lemma implies the cantor bernstein theorem or something like that... I wasn't able to keep up, but I still remember the headaches after the lecture... And I've been too scared to look at the notes I made back then.
@highermathematics-bx4mi2 жыл бұрын
Very amazing 🥰🥰🥰🌹🌹🌹Assalam-o-alaikum may Allah protect you from hardships ameeeeeeeeen
@ezras79975 жыл бұрын
Is there a zenos schilling heel paradox type of thing
@ezras79975 жыл бұрын
Don’t say there is something that ridiculous lol
@edwardhuff47275 жыл бұрын
"Contains" is used as a synonym of "includes." It isn't. A "contains" B when B ∈A. A "includes" B when B ⊂ A. A partially ordered family of sets can be "ordered by inclusion" but "ordered by containsion" is different if it even means anything. A von Neumann ordinal set "includes everything it contains": if B ∈ A then B ⊂ A, or P(A) ⊂ A. where P(A) = 2^A = set of all subsets of A = power set of A. You can't have a set that "contains everything it includes" (Russell's paradox, the set isn't well founded, A ∈ A). The sets of Zorn's lemma are posets, partially ordered, and "ordered by inclusion".
@drpeyam5 жыл бұрын
Ok, but I’ve always learned contained and includes as the same thing. I’d explicitly use B is an element of A
@edwardhuff47275 жыл бұрын
@@drpeyam I found it confusing too, and when I couldn't figure which is which, looking in Halmos Naive Set Theory it's hard to find the definition of "includes." The distinction might be less vital when elements are atoms like { 1, 2 } rather than { {{}}, {{},{{}}} }.
@alexandersanchez91385 жыл бұрын
Also, Dr. Peyam said “circles” instead of “disks.” Indeed, concentric circles don’t contain one another. Alas, it doesn’t really matter because this is an informal (not to be confused with ‘not rigorous’) proof, and we get the gist.
@SierszulskiM5 жыл бұрын
As a Pole I'd just like to mention it would be nice to call the lemma "Kuratowski-Zorn lemma" - Kuratowski came up with it eevn earlier than Zorn, if I'm not mistaken.
@Anteater234 жыл бұрын
Do you do Galois Theory?
@drpeyam4 жыл бұрын
Sadly not at all
@ellobo99994 жыл бұрын
Thank you!
@tarunpurohit65225 жыл бұрын
Lv u docter
@justjacqueline20045 жыл бұрын
I am so ******* dim!Whilst I can follow it I am damned if I could solve a problem requiring this work.
@drpeyam5 жыл бұрын
I agree, me neither! I always get stuck on those problems
@foreachepsilon5 жыл бұрын
Isn't it V not(subset) span(beta)?
@drpeyam5 жыл бұрын
But beta is a subset of V, so span(beta) is a subspace of V
@foreachepsilon5 жыл бұрын
You wrote span(beta) not(subset) V which would imply there is a v in span(beta) not in V but looks like you said there is a v in V not in span(beta), right?
@drpeyam5 жыл бұрын
It’s the latter, there is v in V not in span(beta)
@foreachepsilon5 жыл бұрын
Dr Peyam so wouldn’t that be V not(subset) span(beta) as opposed to span(beta) not(sunset) V then?
@drpeyam5 жыл бұрын
Ooooh, I get the confusion now. I didn’t say span(beta) is not a subset, the notation means span(beta) is a strict subset of V, so span(beta) is a subset of V but not equal to V, so there’s v in V not in span(beta)
@jonasdaverio93695 жыл бұрын
By the way, I hate (some of the) classical proofs. They really make no sense! Per example, you can show you will never find any basis on some vector spaces, but in the same time you know there has to be one. You know for sure it exists, but you know for sure you'll never find it. What is the point of it all?! Constructivism (aka intuitionism) is far superior and more intuitive (who would have thought?).
@drpeyam5 жыл бұрын
Totally agree, I prefer constructivism, but sometimes there’s nothing we can do
@jonasdaverio93695 жыл бұрын
Then talk about it in your videos!
@drpeyam5 жыл бұрын
lol, why? It’s just an opinion, not a mathematical fact, haha. Also I don’t say I don’t like it, sometimes it’s necessary
@jonasdaverio93695 жыл бұрын
There are whole foundations of mathematics based on constructivism. homotopytypetheory.org/book/ It is not a matter of taste. No model is true, some are useful. You can totally imagine mathematics without law of excluded middle. Saying it is necessary is like saying "Sometimes it is necessary to assume A because we want to show A."
@jonasdaverio93695 жыл бұрын
@@drpeyam Since you know French and you seem interested, you should check out a series of video made by Science4all, it is quite old but it thing you should like it: m.kzbin.info/aero/PLtzmb84AoqRRgqV5DfE_ykuGQK-vCJ_0t From the 15th video, it begins to talk almost only about constructivism and why constructivism is better than classical logic.
@highermathematics-bx4mi2 жыл бұрын
My ny gusy wala face dakh kar video on ki thi because mojy bi gusa a raha tha is per😡 Now I am happy🤣🤣🤣🤣😇😇😇
@hyunwoopark92415 жыл бұрын
Thats quite a awesome thumbnail for a mth video
@NitinVerma-nh9vp4 жыл бұрын
Sir plz prove Sylow's 2nd theorem using Zorn's lemma
@newtonnewtonnewton15875 жыл бұрын
Nice video thanks D peyam السلام عليكم رمضان كريم
@Anteater234 жыл бұрын
You look like Kaka footballer.
@waterfirecards51285 жыл бұрын
First!
@drpeyam5 жыл бұрын
Megha Jogithaya It’s been unlisted for a month, that’s why
@jonasdaverio93695 жыл бұрын
@@drpeyam Noooo, you revealed our secret. That's really mean to us! (harmonic mean, not the arithmetic one)