When Studying Maths is UNSATISFYING... [ Math Joke Video ]

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  • เผยแพร่เมื่อ 1 ม.ค. 2025

ความคิดเห็น • 370

  • @AndrewDotsonvideos
    @AndrewDotsonvideos 5 ปีที่แล้ว +1131

    Now I have nothing.

    • @marinmaths3826
      @marinmaths3826 5 ปีที่แล้ว +23

      Lmao, come on wreck him Dr. Dotson!

  • @kamranrachlin2769
    @kamranrachlin2769 5 ปีที่แล้ว +543

    I spent a year studying in Japan (in English) and I swear to god one of the lecturers actually used Japanese letters at variables at one point the madman

    • @simeondermaats
      @simeondermaats 4 ปีที่แล้ว +82

      Was that like
      2な = 4
      な = 2

    • @ladasodaexplains3355
      @ladasodaexplains3355 4 ปีที่แล้ว +56

      I used Chinese characters for integration by parts, I bet my professor was still confused till this day what I wrote on the exam 😂

    • @Kazu-don
      @Kazu-don 4 ปีที่แล้ว +30

      @@ladasodaexplains3355 You just gave me ideas for my exams

    • @achannel9598
      @achannel9598 3 ปีที่แล้ว +7

      @@ladasodaexplains3355 lol which character did you write?

    • @pierfrancescopeperoni
      @pierfrancescopeperoni 3 ปีที่แล้ว +18

      @@simeondermaats な² = 7

  • @willful759
    @willful759 5 ปีที่แล้ว +383

    "a non trivial exercise"
    proofs like this are isomorphic to shitposts

    • @CalBruin
      @CalBruin 5 ปีที่แล้ว +10

      @@PapaFlammy69 what was the textbook from which that non-trivial exercise line appeared?

  • @Davidamp
    @Davidamp 5 ปีที่แล้ว +531

    "Yes, Andrew?" I'm dead

  • @non-inertialobserver946
    @non-inertialobserver946 5 ปีที่แล้ว +608

    Integaral Bruh(威) d威

    • @mmtf
      @mmtf 5 ปีที่แล้ว +79

      its even better because the kanji means intimidating

    • @non-inertialobserver946
      @non-inertialobserver946 5 ปีที่แล้ว +9

      @@mmtf lol

    • @miloradowicz
      @miloradowicz 5 ปีที่แล้ว +13

      I love reading math books in Chinese. Explanations there are just much clearer.

    • @dangernoodle2868
      @dangernoodle2868 5 ปีที่แล้ว +9

      \int_{-\infty}^\infty bruh(ゴゴゴゴゴ) dゴゴゴゴゴ

    • @miloradowicz
      @miloradowicz 5 ปีที่แล้ว +21

      @@dangernoodle2868
      e^(iπ) = - 一
      f(x) = f(零) + x/(一!) + (x^二)/(二!) + (x^三)/(三!) + (x^四)/(四!) + (x^五)/(五!) + …

  • @TheBlueboyRuhan
    @TheBlueboyRuhan 5 ปีที่แล้ว +546

    You know it's good when you say euler twice but differently AND it's an Andrew Dotson parody

    • @hasiumcreeper5384
      @hasiumcreeper5384 5 ปีที่แล้ว +25

      EULERn multiple ways to say mathematicians' names.

    • @EpicMathTime
      @EpicMathTime 5 ปีที่แล้ว +3

      @@hasiumcreeper5384 Underrated comment

  • @parthpawar7837
    @parthpawar7837 5 ปีที่แล้ว +708

    I was prepared was e=2.. heck even for pi=3... But God I wasn't prepared for e=pi

    • @rsg282
      @rsg282 5 ปีที่แล้ว +55

      pi^2 = g

    • @IQuick143cz
      @IQuick143cz 5 ปีที่แล้ว +124

      The complete version is: 4 = π = 3 = e = 2 = Φ = 1 = The points Andrew got

    • @dannygjk
      @dannygjk 5 ปีที่แล้ว

      @@IQuick143cz wtf lol

    • @HDitzzDH
      @HDitzzDH 5 ปีที่แล้ว +11

      pi = sqrt(g)

    • @canriecrystol
      @canriecrystol 5 ปีที่แล้ว +19

      Weak, too weak. Ln(π)=1, fundamental theorem of engineering

  • @MYCHEM1CALR0M4NCE
    @MYCHEM1CALR0M4NCE 5 ปีที่แล้ว +177

    “No way you can use something you’ve used in another course” why is this so true

    • @dragonflyerstern156
      @dragonflyerstern156 5 ปีที่แล้ว +4

      We have luck ouf geometry prof allows us to use Ana 1/2 and LinA 1/2. The reason could be that she is the same prof

    • @jeangtech1830
      @jeangtech1830 5 ปีที่แล้ว

      Fr bro

  • @shellrox2878
    @shellrox2878 5 ปีที่แล้ว +216

    "Fundamental Theorem of Engineering", lol!

    • @livedandletdie
      @livedandletdie 5 ปีที่แล้ว +19

      It works though. e=2 pi=3 and e=pi and sinx=x and cosx=1 you just have to write a small enough x preferably 0

    • @shellrox2878
      @shellrox2878 5 ปีที่แล้ว +2

      @@livedandletdie x = lim x -> 0 (x)

    • @erikkonstas
      @erikkonstas 5 ปีที่แล้ว

      @@livedandletdie dx outside the denominator.

  • @ayeshas6580
    @ayeshas6580 5 ปีที่แล้ว +159

    Derive "wheelers" formula haha

  • @ClaireYunFarronXIII
    @ClaireYunFarronXIII 5 ปีที่แล้ว +89

    “Mr. Dotson?”
    “Yes, Andrew.”
    I UNDERSTOOD THIS VERY WELL! 😂

  • @trueperson-o2z
    @trueperson-o2z 5 ปีที่แล้ว +69

    "You're going to give a talk about Inter universal Teichmüller Theorem, you may have heard about it, it's pretty trivial". Bruh.

  • @thenukex1268
    @thenukex1268 5 ปีที่แล้ว +51

    The 1 page proof with 2 pages of references had me dead

  • @x0cx102
    @x0cx102 5 ปีที่แล้ว +33

    "Mandatory stats class that everyone has to take"
    AHAHAHAHAHAHA
    My brilliant math friend is suffering through this right now at college

  • @peregee
    @peregee 5 ปีที่แล้ว +114

    I'm defining my next function as bruh(e)

  • @SakraIgor0qNomoko
    @SakraIgor0qNomoko 5 ปีที่แล้ว +27

    45 of 48 points were docked because you proved the exercise using a general LCH space instead of exactly R. The remaining two were for spending too many lines on a clearly trivial matter.

  • @ariuwu1234
    @ariuwu1234 5 ปีที่แล้ว +44

    Wheeler's formula and Yuler's identity
    cool

  • @OllysGaming777
    @OllysGaming777 5 ปีที่แล้ว +104

    Bruh I rate this a e/π 🔥👌🔥👌🔥

  • @luck3949
    @luck3949 5 ปีที่แล้ว +13

    4:33 Oh! Now everything makes sense. That 3=2 discount advertisements were just using pretty advanced math.

  • @aflah7572
    @aflah7572 5 ปีที่แล้ว +152

    When Netflix Adapts A Manga 😂

  • @henrikrynauw244
    @henrikrynauw244 4 ปีที่แล้ว +16

    There is nothing worse than the good old "This part is left as an excersise for the reader." .

  • @jaspergodfreyzann5421
    @jaspergodfreyzann5421 5 ปีที่แล้ว +84

    Integharal of bruh with respect to moment

    • @schokoladenjunge1
      @schokoladenjunge1 5 ปีที่แล้ว +5

      the bruh moment of a probability distribution

  • @OlliWilkman
    @OlliWilkman 5 ปีที่แล้ว +8

    I remember a proof from a textbook along the lines of, "With a bit of algebra, we see that the right side can be written as…" and then spending about three hours unsuccessfully trying to work out how it's done.

    • @dannygjk
      @dannygjk 5 ปีที่แล้ว +3

      "bit of algebra" XD

  • @pinec0ne
    @pinec0ne 5 ปีที่แล้ว +57

    4:32
    Actually, as an engineering student, I can confirm that the real fundamental theorem of engineering is
    Lim_[GPA->0] (Engineering) = Business
    (Stolen from Reddit)

  • @gunhasirac
    @gunhasirac 5 ปีที่แล้ว +89

    “I’m trying this for 45 minutes straight going nowhere”
    That doesn’t sound long lol
    You can get lost with a problem with 5 hours.

    • @이준혁-c4s
      @이준혁-c4s 3 ปีที่แล้ว +2

      Hours? Well it may be days with algebra

    • @Isa-tn7ex
      @Isa-tn7ex 3 ปีที่แล้ว

      If it’s a meaty problem, regardless of type, it’s weeks or months- and in the best cases, years :D

  • @SuperMiketron
    @SuperMiketron 5 ปีที่แล้ว +29

    This video is like one big shitpost. I love it.

  • @ValoriYT
    @ValoriYT 3 ปีที่แล้ว +1

    You switched from "yooler" to "wheeler" for "Euler" both in the same sentence, and even though it's a part of the joke, it is very frustrating lol

  • @alse72
    @alse72 5 ปีที่แล้ว +26

    Kanji math notation sounds sicc, do it!

  • @mayankvats926
    @mayankvats926 5 ปีที่แล้ว +21

    Andrew Dotson should definitely see t'is. Lmao

  • @ilonachan
    @ilonachan 5 ปีที่แล้ว +9

    About the Kanji thing: aren't we actually running out of Greek letters by now? Aren't ~15,000 Japanese characters a good solution? I mean, you don't need to know what the characters mean to use them as variable names. And if you do know what they mean, you can actually have meaningful variable names _in math!_

  • @neilgerace355
    @neilgerace355 5 ปีที่แล้ว +43

    Good MORNING fellow mathematicians!
    I suspected something was up when I saw the glasses: Papa is trying to make himself look smart. A venture doomed to failure :p

  • @calvinlee96
    @calvinlee96 5 ปีที่แล้ว +5

    As a math undergrad it hits me hard to see all my notes filled with theorem and lemmas while their proofs are left as an exercise...

  • @robertlauff8791
    @robertlauff8791 5 ปีที่แล้ว +3

    There is a package (xeCJK) that allows you to use Kanji, Hiragana, Katagana, Korean etc in Latex(XeTex to be precise) and it drives people correcting your homework crazy, espeacially if you use it in linear algebra ;D

  • @anthonynorman7545
    @anthonynorman7545 5 ปีที่แล้ว +7

    I died at "check for symmetry." Hits too close to home.

  • @x0cx102
    @x0cx102 5 ปีที่แล้ว +4

    Discovered your channel recently and this is one of the funniest videos
    Your collabs with Mr Dotson are also very on point!

  • @donati880
    @donati880 5 ปีที่แล้ว +11

    Mr.Dotson i've got a question! Lost it there hahahahahahahah

  • @programaths
    @programaths 4 ปีที่แล้ว +3

    At university, got a teacher who wrote a "-" in a formula and get with it for the end of the lesson. So, I raised my hand and told him it should be a "+". He replied that I was not correct.
    When leaving the room, he crossed the "-" to make it a "+"...I was right and he didn't want to give me credits and wanted to mess with me.
    The thing is that it pissed me twice because I was thinking of others too. But the truth is that it was a detail that everyone would forget.
    School is not only about the material. It's also a place to learn that you have to deal with things that are unjust and unfair. Life is neither "just" and "fair", it's random.

  • @completeandunabridged.4606
    @completeandunabridged.4606 5 ปีที่แล้ว +64

    You-ler

    • @completeandunabridged.4606
      @completeandunabridged.4606 5 ปีที่แล้ว

      @@PapaFlammy69 do you know of the fundamental theorem of amateur engineering?

    • @rafciopranks3570
      @rafciopranks3570 5 ปีที่แล้ว +1

      Oiler

    • @___xyz___
      @___xyz___ 5 ปีที่แล้ว +1

      Owler

    • @MattixHQ
      @MattixHQ 5 ปีที่แล้ว +1

      @@PapaFlammy69 I think '' wheeler'' is best xD

  • @dontsmackdafish3771
    @dontsmackdafish3771 4 ปีที่แล้ว +4

    Professor- "Compactness- ever open cover admits a finite sub cover"
    me- "what?"
    Professor-"Got that? Ok, moving on"

  • @josepha.cardenas9168
    @josepha.cardenas9168 4 ปีที่แล้ว +6

    "THe Proooof is trUVIal and left as a more trivial exercise".
    *Checks the book and reads 3 more.
    Holy 🐄...
    I am John Snow.

  • @sergeitikhomirov9780
    @sergeitikhomirov9780 5 ปีที่แล้ว +74

    No jokes about Frog Toadwalker, but ok

    • @nafissaatlagh206
      @nafissaatlagh206 5 ปีที่แล้ว +4

      I rly dont understand whats ur problem with dat guy can u explain pls 😐😐😐😐

    • @UrasSomer
      @UrasSomer 5 ปีที่แล้ว +6

      @@nafissaatlagh206 😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐😐

    • @defunct1373
      @defunct1373 5 ปีที่แล้ว +6

      @@nafissaatlagh206 r/woooosh

    • @sergeitikhomirov9780
      @sergeitikhomirov9780 5 ปีที่แล้ว +27

      Sas Kia sure, but before i do...Can you figure it out? Give this problem a try

    • @nafissaatlagh206
      @nafissaatlagh206 5 ปีที่แล้ว

      Hahaha cant u just answer directly lol I mean m not a big follower of his but I've seen papa flammy trollin him in his videos several times n I wanna understand pliis 😐😐😐😐😭😭

  • @wikiwikitoria
    @wikiwikitoria 5 ปีที่แล้ว +28

    nailed the british accent boi

    • @fireflyrobert
      @fireflyrobert 4 ปีที่แล้ว +3

      I agree and I'm a Brit

  • @thepositron5676
    @thepositron5676 5 ปีที่แล้ว +17

    "The Fundamental Theorem of Engineering" "Wheeler" "Youler" lmao XD

  • @absolutelymath3399
    @absolutelymath3399 5 ปีที่แล้ว +7

    Wow! This is great hahahahaha! Even loved the mandatory statistics haha

  • @modestorosado1338
    @modestorosado1338 5 ปีที่แล้ว +2

    Damn those "the proof is left as an excercise to the reader" theorems. I often picture the author thinking "hmmmm, this proof is hard as nails. Oh, well I'll just leave it as an excercise just to fuck with the reader". And then proceed to laugh their ass off while they keep writing.

  • @awez_mehtab
    @awez_mehtab 3 ปีที่แล้ว +2

    Lol he said yooler and wheeler

  • @gagers78
    @gagers78 5 ปีที่แล้ว +2

    Bruh this is pretty good. The one at the start was the best imo.

  • @hoodedathlete6626
    @hoodedathlete6626 5 ปีที่แล้ว

    This is so amazing. Love it. Keep up the good work!

  • @ragerecords2476
    @ragerecords2476 4 ปีที่แล้ว +4

    "Youlers formula and wheelers identity" some time you just nail it in the very beginning.hats off sir, it was brilliant
    I like the guy who holds his shirt down btw, what is that supposed to mean ?

  • @bop2864
    @bop2864 4 ปีที่แล้ว +1

    Isn't Euler's pronounced as Oiler's? but maybe that was part of the joke

  • @MrXenon-hn7ju
    @MrXenon-hn7ju 5 ปีที่แล้ว +7

    1 out of 48 points! Why have I once again received 1 out of 48 points!?!?!?!?!?!?

  • @noname_whatsoever
    @noname_whatsoever 5 ปีที่แล้ว +1

    'It's very trivial, only one page.' Yeah. You're not fooling anyone, I'm not a child anymore, bruh.

  • @bramlentjes
    @bramlentjes 5 ปีที่แล้ว +1

    Hahahahahahaa super papa!!! The Teichmuller part was wonderful!

  • @kayleenmedina7889
    @kayleenmedina7889 5 ปีที่แล้ว +5

    4:15 Oh MY GOD.
    I felt that lol
    That statement was 100% true.
    I’m happy I chose applied mathematics. Ha

  • @jonaargueta771
    @jonaargueta771 4 ปีที่แล้ว +3

    2:43 you can use the symetry/antisymetry argument only if you now the parity of bruh(z(x))

  • @tomasblovsky5871
    @tomasblovsky5871 5 ปีที่แล้ว +4

    Papa Flammy: "So students, here's the new exercise SHIIIIIT" ... students: "oh that was a good SHIIIT".

  • @wiener_process
    @wiener_process 3 ปีที่แล้ว +1

    I've literally had to learn how to write Schwabacher M in measure theory. It was the hardest part of that class, and that says something.

  • @kwirny
    @kwirny 5 ปีที่แล้ว

    I immediatly sent this my friends, you are so genius.Keep up the good work.

  • @legendhero-eu1lc
    @legendhero-eu1lc 4 ปีที่แล้ว

    Thank you for the video! All of you friends are super awesome! Oh, moments with this video are sad.

  • @luck3949
    @luck3949 5 ปีที่แล้ว +2

    That symmetric integral thing is so relatable :'D

  • @DavidPumpernickel
    @DavidPumpernickel 4 ปีที่แล้ว

    @flammable maths papa flammy is the hard drive on the shelf at 3:43 the same one you pull out in one of your most recent videos? you call it a hard drive anyway

    • @DavidPumpernickel
      @DavidPumpernickel 4 ปีที่แล้ว

      und na ja du sagst ich glaub 'have a hard driven day'

  • @sortsome
    @sortsome 5 ปีที่แล้ว +2

    "I'm so glad you're finally doing something right in your life. That you are doing a math course... for once."

  • @Uriakatos
    @Uriakatos 3 ปีที่แล้ว +1

    I screenshot the nontrivial exercise shot from 7:13. Absolutely fucking hilarious.

  • @SteveDice21
    @SteveDice21 4 ปีที่แล้ว

    3:13 It's even worse when you're supposed to know something that is taught in a course that's nowhere listed as a prerequisite for the course you're taking.

  • @georgelsgomes9634
    @georgelsgomes9634 5 ปีที่แล้ว +5

    I love linguistics... yeah!A veeeery old professor around here always spoke some shit in Latin in our classroom.. then I studied some Latin and later ancient Greek. I always... ALWAYS talk about this. I'll never forget about that fvcking lambda calculi book with Hebraic signs.. I felt "god dammit! wat I'm doing in my life!". we don't have enough symbols to "speak" mathematics lulz

  • @eirikkvalheim8627
    @eirikkvalheim8627 5 ปีที่แล้ว +3

    This was absolutley spot on and hillarious! As a Math student there is too much relatable content here xD

  • @dannygjk
    @dannygjk 5 ปีที่แล้ว +4

    I would hate to take non-trivial math courses. O.O

  • @shadownik2327
    @shadownik2327 2 ปีที่แล้ว +1

    My god I remember that symmetry on the integrand, they did give the explanation and hint but u refused to see it, I was so frustrated and at the same confident and i finally did end up looking at the hint though. I still can't believe I was that petty😅

  • @dns911
    @dns911 4 ปีที่แล้ว +1

    6:34
    6:45
    pi^3 = 69?
    Are we in engineering class here or what?

  • @emilyscloset2648
    @emilyscloset2648 5 ปีที่แล้ว +1

    I lost it when u introduced the fundamental theorem of engineering around 4:30 ish

  • @cmilkau
    @cmilkau 4 ปีที่แล้ว +6

    The biggest disappointment for me, and I guess not just for me, was to learn about foundations of mathematics. Eg. the set theory crisis and while there was considerable effort put into unraveling the story, most of mathematics just went on with ZFC (which is really just turning your wishes into a definition) and be done with it. Also Gödel's incompleteness theorems and how little (successful) investigation happened after that. It seems that foundations of mathematics are so hard that the brightest minds will find the inconsistencies, but noone can unravel the structures.

  • @jdd109
    @jdd109 5 ปีที่แล้ว +1

    That English (??) Accent was hilarious he sounds just as distressed and ill as me in my head in a test when I can't answer the first page

  • @milan6193
    @milan6193 4 ปีที่แล้ว +1

    trust me as someone who's taken 4 years of japanese you are gonna want to start using weird fish drawings for variables-

  • @tanvec
    @tanvec 5 ปีที่แล้ว +4

    I always called Xi "the tornado" and I was hoping for a mathematical hadouken when I got into grad school

  • @tauceti8341
    @tauceti8341 4 ปีที่แล้ว

    7:12 And his name was JOHN CENA?!!!
    Are you getting me right now, are you kidding me right now?

  • @Gameboygenius
    @Gameboygenius 5 ปีที่แล้ว +4

    Should have been "Yes, Steven?" :p

  • @ja-vishaara
    @ja-vishaara 3 ปีที่แล้ว

    7:05 Page number pi? That sure doesn't look like the third page of the book

  • @KazACWizard
    @KazACWizard 3 ปีที่แล้ว

    4:01 i really felt that. i have to do mandatory statistics and it is the worst.

  • @moskthinks9801
    @moskthinks9801 5 ปีที่แล้ว +6

    2:09 smart people (flammy) love andrew
    Owo

  • @OtiumAbscondita
    @OtiumAbscondita 5 ปีที่แล้ว +5

    The first time is always a but awkward...

  • @MKWKezer
    @MKWKezer 5 ปีที่แล้ว +1

    I‘m stuck at the Applied Math scene at the moment in my studies lol.

  • @tommyv1262
    @tommyv1262 5 ปีที่แล้ว +14

    Hate your shirt btw. Everytime prof says that something is trivial I get triggered.

    • @dannygjk
      @dannygjk 5 ปีที่แล้ว +2

      Yes it's a form of PTSD ;)

  • @kenzilamberto1981
    @kenzilamberto1981 4 ปีที่แล้ว +1

    Where is that one page paper of IUT lol?

  • @grimztherapist
    @grimztherapist 5 ปีที่แล้ว +2

    1 out of 48 points hits too close to home :(

  • @suspendedsuplexchannel1000
    @suspendedsuplexchannel1000 5 ปีที่แล้ว +4

    I wrote in exam "Euclid's idendity"😂😂

  • @Israel2.3.2
    @Israel2.3.2 5 ปีที่แล้ว +3

    "2 months later..." [spongebob voice]

  • @IkEisawesome7
    @IkEisawesome7 5 ปีที่แล้ว +2

    Ah yes, the classic Wheeler-Youler formula!

  • @grammatikerfanatiker
    @grammatikerfanatiker 4 ปีที่แล้ว

    How do you recommend that book? Kern- und Elementarteilchenphysik? It says it’s from 1988, do you find that it is still good?

  • @enochsadventures
    @enochsadventures 5 ปีที่แล้ว +1

    >mfw wanting to study pure maths
    "Hi, this is McDonalds. Can I take your order?"

  • @TheYoshi463
    @TheYoshi463 5 ปีที่แล้ว +7

    Was erwartest du auch von einem Buch über Physik?^^

    • @schokoladenjunge1
      @schokoladenjunge1 5 ปีที่แล้ว

      u fkcn w0t m0? i'll have you know i graduated top of my class at physics university. [insert physics rant here][insert fortnite slang here] [insert value of X here] you're an existence proof to me, kiddo. Trivial and only mathematicians acknowledge it.

  • @ericl8743
    @ericl8743 5 ปีที่แล้ว +4

    "It happens every damn week" 😂😂

  • @iiFiingkSoo
    @iiFiingkSoo 3 ปีที่แล้ว

    Just discovered your channel. Literally ROFL ❤️😂
    *Subscribed

  • @69erthx1138
    @69erthx1138 5 ปีที่แล้ว +3

    Schlagen Sie den Dollar-Laden für Verkleidungen Boi

  • @domenicopiegaia7816
    @domenicopiegaia7816 5 ปีที่แล้ว +1

    neat editing

  • @atomicsight603
    @atomicsight603 2 ปีที่แล้ว +1

    Wheeeeeler!

  • @bensalemmohamedabderrahman5844
    @bensalemmohamedabderrahman5844 4 ปีที่แล้ว +2

    4:33 greatest one everrrrr.

  • @JPK314
    @JPK314 5 ปีที่แล้ว

    K_x is a subset of S: trivial
    The operation is associative: trivial
    The restriction of the operation to K_x gives a subset of K_x: two elements x^a and x^b for r≤a,b≤r+p-1 have x^a•x^b := x^(a+b). If a+b≤r+p-1 then r≤a+b≤r+p-1 so x^(a+b) is in the set. Else a+b≥r+p because a,b,r,p are all integers, so the proof proceeds as follows: r+p≤a+b≤r+r+p+p-2 so r≤a+b-p≤r+p-2≤r+p-1 but x^(a+b)=x^(a+b-p) by definition of p (specifically, a+b-p≥r as per our assumption in the else portion of this proof) so because x^(a+b-p) is in the set, the set is closed under the operation.
    K_x contains an identity element: trivial (by definition it is x^r)
    K_x contains an inverse element for every element in the set: trivial (for a given element x^a for r≤a≤r+p-1 its inverse is x^(r+p-a))

  • @sriniwasj
    @sriniwasj 5 ปีที่แล้ว

    Man I'm living for this shit now

  • @CrittingOut
    @CrittingOut 5 ปีที่แล้ว +1

    4:32 fundamental theorm of engineering