Relation Between Infinite Sums and Products: Convergence Conditions

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  • Опубликовано: 30 янв 2025
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Комментарии • 73

  • @zunda-theorem-en
    @zunda-theorem-en  3 месяца назад +98

    Thank you so much for watching and for all your valuable feedback!
    I've heard mixed opinions on the English dubbed version, and I noticed some of you prefer the original Japanese audio, so I decided to bring back the Japanese audio with English subtitles. However, managing both requires additional work, and there’s a chance RUclips might not favor this approach, so I may need to decide between keeping the English subtitles on the Japanese version or continuing with the English dubbed version in the future.
    For now, I'll continue to provide both, and I'll keep listening to your feedback. Thank you again for your support!

    • @zunda-theorem-en
      @zunda-theorem-en  3 месяца назад +20

      I tried to pin my comment, but I don't have permission since this channel was recently created...

    • @MushiSaad1
      @MushiSaad1 3 месяца назад +10

      Maybe try some sort of community poll in your main channel

    • @josephbrandenburg4373
      @josephbrandenburg4373 3 месяца назад +18

      I never would have discovered this if it weren't for the English version, and I watch a LOT of math videos. I think youtube mostly only shows videos to people who speak the language of the video

    • @andersonm.5157
      @andersonm.5157 2 месяца назад +3

      I just found your channel and it's fantastic. I usually don't like English dubbing, but in this case the dubbing was really good and natural. Even though English is not my native language, I found it easier to follow the English version.

    • @mmendezanahuac
      @mmendezanahuac 2 месяца назад +1

      Hi, thank you for the great work.
      In my subjective preference, I'd rather prefer a lower volume for the background music, because it is very distracting.
      Everything else is superb.
      Great work! Thanks!

  • @kintingkam6704
    @kintingkam6704 2 месяца назад +24

    Anime girl in her cutest voice "So~ what's today problem~??" *Proceed to explain high end mathematics*

    • @kingeternal_ap
      @kingeternal_ap 2 месяца назад +4

      Not really high-end.
      I mean, the "bounded by" definition is missing, but hey, at least there is no calculus here

    • @lavinissensonthecommenter4197
      @lavinissensonthecommenter4197 2 месяца назад

      I wouldn’t say calculus is hard

    • @kaidatong1704
      @kaidatong1704 Месяц назад

      0:41 I was so paranoid of getting jumpscared with a "what the sigma?"

    • @kaidatong1704
      @kaidatong1704 Месяц назад +1

      btw I don't actually care about the math. just had too much of the romance genre lately and sought to restore balance by listening to a regular conversation that feels like normal school days but grounded at least

    • @kaidatong1704
      @kaidatong1704 Месяц назад

      @@kingeternal_ap I did a quick search and got "denoting the most expensive of a range of products"(range not as opposed to domain and products not as in result obtained from multiplication ... get your mind out of the math gutter) as the definition of "high-end". I guess it's just 1on1 tutoring being more expensive than going to public school which are government funded. and even if you're thinking about which grade level, if u metaphorically squint a bit u can imagine zundamon looking like they're in kindergarten and this has got to be above that

  • @constantinbouet4052
    @constantinbouet4052 2 месяца назад +18

    I love this anime-mathematics mix

  • @weegee7924
    @weegee7924 3 месяца назад +51

    The dub is fantastic! Although, it would be nice to have English subtitles on the JP videos for those who prefer it 🙏

  • @ガーリック-v6y
    @ガーリック-v6y 3 месяца назад +67

    英語版のずんだもんの声を初めて聞いた

    • @jalmar40298
      @jalmar40298 3 месяца назад +5

      メトゥン…(Native)

    • @matsubarahijiri
      @matsubarahijiri 3 месяца назад +1

      @@jalmar40298 日本語版のチャンネル発見
      英語と数学を同時に勉強できる良い教材

    • @Yubin_Lee_Doramelin
      @Yubin_Lee_Doramelin 3 месяца назад +7

      Welcome to English version of Zundamon's Theorem! However, due to grammatical difference between Japanese and English, you can't listen to Zundamon saying "なのだ" on every end of sentences - which is her identity...

  • @smashingstuff2454
    @smashingstuff2454 23 дня назад +2

    I always wanted to learn how to solve infinite product. This video taught me a lot, thank you

  • @pichirisu
    @pichirisu 2 месяца назад +9

    Now do this for the entirety of mathematical statistics, thanks.

  • @angrykirby_yt
    @angrykirby_yt 3 месяца назад +22

    Thank you for the English dub but as an anime fan, I prefer reading subtitles on the original version 😅

  • @takumamori7092
    @takumamori7092 3 месяца назад +14

    ずんだもんで英語が扱えるの初めて知った

  • @Grassmpl
    @Grassmpl 4 дня назад +1

    This would have helped back when I took analytic number theory in my undergrad.

  • @cdkw2
    @cdkw2 3 месяца назад +2

    Love that you are posting on a english channel now

  • @InternetCrusader-rb7ls
    @InternetCrusader-rb7ls 3 месяца назад +1

    This is really well put together.

  • @TheOneWhoHasABadName
    @TheOneWhoHasABadName 3 месяца назад +10

    Zundamon and Metan speaking in english sounds a little bit weird, and I like it
    though, the English subtitles + Japanese speech does make it feel a bit more like anime, and it might be more convenient for you too. I'm fine with any arrangement as long as the English subtitles still remain in some form, voice is just a bonus

  • @PotatoImaginator
    @PotatoImaginator 3 месяца назад +1

    Thanks for making English one :)

  • @quannguyenminh4236
    @quannguyenminh4236 3 месяца назад +7

    Please keep both english dub channel and english subtitle in japanese channel, although I dont like the english dub so much but I still enjoy listen the lesson when i am do something else.

  • @RadicalCluster
    @RadicalCluster 2 месяца назад +1

    Thanks zundamon

  • @xmearionet
    @xmearionet 3 месяца назад +13

    I personally prefer japanese voice + subtitles (partially because the japanese voices dont sound generated but sound real)

  • @magma90
    @magma90 3 месяца назад +3

    5:25 i will be using that notation from now on

  • @thedude882
    @thedude882 2 месяца назад +2

    You can prove the sum converges iff the product converges by showing that the sum a_n converges iff sum log(1+a_n) converges. The latter can be showed through the ratio test. But the sum log(1+a_n) converges iff exp(sum(log(1+a_n))= prod(1+a_n) converges.

  • @ftiasch
    @ftiasch 3 месяца назад +5

    Thank you for the video as always. However, I must state that I prefer the previous combination of Japanese voices and English subtitles (I had thought it was also translated by RUclips). Is there a possibility for us to continue with the old method?

  • @ryosuke8093
    @ryosuke8093 3 месяца назад +1

    I was surprised that you also made an English version.

  • @kaidatong1704
    @kaidatong1704 Месяц назад +1

    12:54 a way to help remember it is to use the somewhat-pun think "absolutely" as measure of certainty, like you're 100% sure that smth is true. mnemonics are allowed to be nonsense so it's fine

    • @kaidatong1704
      @kaidatong1704 Месяц назад

      ugh, my head got fuzzy from trying to binge these and I just noticed my attention span is so low I get distracted every minute (judging by frequency of random comments I've been spamming)

  • @whyre69
    @whyre69 3 месяца назад +2

    this channel is amazing, thank you for making the english version

  • @kaidatong1704
    @kaidatong1704 Месяц назад +1

    10:44 after getting invested enough to care about this character and watching the (this doesn't feel like the right word for it but whtv) self-referencing culture guide vid, I can't help but think shrek intro song with instance of "tool in the shed" replaced with "arrow in the quiver"

  • @MushiSaad1
    @MushiSaad1 3 месяца назад +11

    I think japanese dub with anime sub is better

  • @gnt10
    @gnt10 2 месяца назад +1

    I didnt expect to see something like this😅

  • @koicc1192
    @koicc1192 3 месяца назад +1

    I don't get convergence of series and sums but....was pretty exciting

  • @Thesaddestmomentinourlives
    @Thesaddestmomentinourlives 3 месяца назад +1

    Thanks a bunch

  • @kingeternal_ap
    @kingeternal_ap 2 месяца назад +1

    Brain.exe stopped working

  • @zyansheep
    @zyansheep 3 месяца назад +8

    I'm not used to dubbed anime 😭
    any chance we could have subs on the original video? Also, I enjoy reading the japanese comments by pressing the translate button...

  • @SuperChumps
    @SuperChumps 3 месяца назад +5

    I actually like the English audio + english sub. But the speed of talking is a little slow, which makes them sound more robotic. The english dub sounds better to me at 1.25x speed.

  • @tralomine
    @tralomine 3 месяца назад +7

    I can read english but not listen, the auto generated subtitles are always trash on youtube, please just leave the english subtitles on the japanese audio >_

  • @aguyontheinternet8436
    @aguyontheinternet8436 2 месяца назад +3

    What music do you use for your videos? Very relaxing

  • @AshifKhan-sn6jx
    @AshifKhan-sn6jx 3 месяца назад +4

    I love anime girls teaching math
    (Can you vary different background music in future videos to spice things up? The usual one is starting to get old imo)

  • @alphazero69
    @alphazero69 2 месяца назад +3

    Could you make some videos on easier math problems? That would really help a 10th grader like me 🙃

  • @penguincute3564
    @penguincute3564 2 месяца назад +1

    Adding a_1 to a_n implies a_1 + a_n
    However, if you talking about a finite series, say: Adding a_1, a_2 etc. to a_n together

  • @illumexhisoka6181
    @illumexhisoka6181 2 месяца назад +1

    13:10 but doesn't the convergence of the sum imply the convergence of the product (them without the absolute value) but not the other way around
    Or am i wrong
    I think I remember reading a proof of this some where

  • @terdragontra8900
    @terdragontra8900 3 месяца назад +2

    13:12 I’d like if you gave examples for the failure of this implication, in each direction. Assuming they aren’t super difficult

  • @Nevermind445
    @Nevermind445 3 месяца назад +3

    The internet has ruined me... I cant listen to an anime girl saying 🗿Sigma🗿 without laughing

  • @kevincsellak296
    @kevincsellak296 3 месяца назад +3

    It's slightly weird to actually hear the intonations and pronunciations in a language I'm fluent in; in Japanese, I'm not able to hear when it doesn't sound completely natural, but it is possible here. Nonetheless, the writing's near-impeccable (as were the subtitles before).

  • @jkloe
    @jkloe 3 месяца назад +7

    zundamoan

  • @alibowman862
    @alibowman862 7 дней назад +1

    3
    2
    1
    Go!!!!

  • @b748wkgndu
    @b748wkgndu 3 месяца назад +1

    Please embed the JP ver's URL on the descriptions.

  • @dracoteu2526
    @dracoteu2526 3 месяца назад +1

    5:23 LMAO

  • @deatharim
    @deatharim 3 месяца назад +1

    gaussian integral pls

  • @ethanliu-y2t
    @ethanliu-y2t 3 месяца назад +1

    What is the background music?

    • @zunda-theorem-en
      @zunda-theorem-en  3 месяца назад

      [BGM]
      かえるのピアノ dova-s.jp/bgm/play568.html
      ほのぼのワルツ【リコーダー】 commons.nicovideo.jp/works/nc116360

  • @sleepntsheep1169
    @sleepntsheep1169 3 месяца назад +2

    OMGGGGGG

  • @machazard
    @machazard 3 месяца назад +2

    ボイボって英語喋らせられるんでしたっけ?

    • @zunda-theorem-en
      @zunda-theorem-en  3 месяца назад +3

      概要欄に記載していませんでしたが、他のツールと組み合わせています。

    • @machazard
      @machazard 3 месяца назад +1

      そういう技があるのですね。ありがとうございます。

    • @machazard
      @machazard 3 месяца назад +1

      その技というのはどういうものでしょうか?差し支えなければ教えていただけるとありがたいです。

    • @zunda-theorem-en
      @zunda-theorem-en  3 месяца назад +1

      お手数ですが、RUclips上で動画を探してみてください。
      他にも挑戦している方がいらっしゃるようです👍