Some Small Ideas in Math: A Set of Measure Zero Versus a Set of First Category (Meager Sets)

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  • เผยแพร่เมื่อ 1 ธ.ค. 2024

ความคิดเห็น • 17

  • @nanditasudhatiwari1332
    @nanditasudhatiwari1332 4 ปีที่แล้ว +1

    Subscribed because of two reasons-
    1. Mathematics
    2. True hard work.
    So the channel deserves to grow.
    Good Luck for your PhD. 🙏🏻( Namaskar) 🇮🇳

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว

      I’m glad you found a reason to subscribe and I appreciate the support!! Well wishes in your endeavors as well😁

  • @narutosaga12
    @narutosaga12 3 ปีที่แล้ว

    Bro your videos are a gold mine!! Please don’t stop making them! Wish you the best of all success

    • @CHALKND
      @CHALKND  3 ปีที่แล้ว

      I'm still at it haha! Glad you are enjoying them. 🙂

  • @Santi._.403
    @Santi._.403 4 ปีที่แล้ว +1

    I love these videos, I've barely seen videos this year because of uni, but I wish you the best, good luck with the move!

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว +1

      I’m glad you’re enjoying my stuff!! Thanks for the well wishes!

  • @likestomeasurestuff3554
    @likestomeasurestuff3554 4 ปีที่แล้ว +1

    Can you recommend a place to buy chalkboards at? Or is it feasable to assemble one at home even with a tight schedule?

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว

      Oh gosh, I don’t have any recommendations. Honestly, the first chalkboard was just a piece of book board (for making book bindings) and some chalkboard wallpaper stuck on top of it. It was not at all a good board and only works with certain kinds of chalk but it only cost me 10$ to assemble. The new chalkboard came into the picture by luck, after graduating from undergrad I kinda just stumbled upon the board on clearance at a craft store for around 40$ while out running some errands with my parents. I don’t think it’s real chalkboard slate either, but it does do the job. Real slate is pretty hefty in price and weight from looking from time to time they can be anywhere from 350$ and up, even though my board works for me now, I don’t know if I’ll have a truly informed recommendation until I’ve invested a bit more in this channel! 😅

  • @YorkiePP
    @YorkiePP 4 ปีที่แล้ว

    "why not, it's math" well said :)
    great video, I'm slowly learning more and more about measure theory by just watching internet videos so hopefully by the time I actually take it I'll be ready for how hard it is ^^

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว +1

      Haha well, i'm glad you enjoyed it. Measure Theory can really bend the intuition, which is one of the reasons I'm a fan, but it can also make it difficult at times when first encountering it.

  • @hideyoshitheturtle
    @hideyoshitheturtle 4 ปีที่แล้ว

    Another awesome video! How did you get started with measure theory and category theory? Any recommendations?

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว +1

      Thanks Shuto! Measure theory was introduced to me at the end of my sophomore year of undergrad during my second course in (proof based) real analysis, while some of the concepts of Baire category came up during my first courses in analysis and topology and then again in passing in the measure theory course. (I'm guessing Baire category is the right way to talk about the notions of category I mention in this video. "Category Theory" usually refers to some pretty algebraic "abstract nonsense" as mathematicians often joyfully call it which is also very cool but unrelated to the content/scope of this video)
      IMO having some foundation in real analysis can help with approaching the counter-intuitive examples that I talk about here and that can arise in a more general context when talking about measures or Baire category. If you're interested in digging in more, and have the necessary analysis background I'd recommend diving into an intro to measure theory class/text first since the Baire category stuff appears in a few different contexts and can be harder to nail down without a more eclectic mathematical background.

  • @merbst
    @merbst 4 ปีที่แล้ว

    Huge small ideas!

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว +1

      They are pretty huge aren’t they 😂😅

  • @likestomeasurestuff3554
    @likestomeasurestuff3554 4 ปีที่แล้ว

    Btw loved this video :)

    • @CHALKND
      @CHALKND  4 ปีที่แล้ว

      Glad you did!

  • @freddyfozzyfilms2688
    @freddyfozzyfilms2688 2 ปีที่แล้ว

    category :(