All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis

แชร์
ฝัง
  • เผยแพร่เมื่อ 5 ก.พ. 2025

ความคิดเห็น • 12

  • @WrathofMath
    @WrathofMath  2 ปีที่แล้ว +2

    NOTE: Around 08:58 when we discuss the closure of a set, I must clarify that the closure of A being a closed set is not as trivial as I made it sound. Certainly the closure of A contains the limit points of A, but when unioning A with L, it is possible we introduced NEW limit points of the set L, and thus to show the closure of A is closed, we'd need to consider this possibility. As it turns out, new limit points will not be introduced in this process, so closures are indeed closed, but again - it's not as trivial as I made it sound.

  • @kanikgupta22
    @kanikgupta22 2 ปีที่แล้ว +2

    Your lectures have definitely helped me a lot in these proofs in discrete maths

    • @WrathofMath
      @WrathofMath  2 ปีที่แล้ว

      Glad to hear it! Thanks for watching and let me know if you have any video requests!

  • @FAITHMUMBE-qe6jv
    @FAITHMUMBE-qe6jv หลายเดือนก่อน

    You have been my refuge 😅

  • @TranquilSeaOfMath
    @TranquilSeaOfMath 10 หลายเดือนก่อน

    5:31 I like that you connected your discussion here with closure under an operation.

  • @paladin1147
    @paladin1147 ปีที่แล้ว

    Legend man, legend man

  • @shambo9807
    @shambo9807 ปีที่แล้ว +4

    Saving lives...

    • @WrathofMath
      @WrathofMath  ปีที่แล้ว +2

      I'm doing my best! Let me know if you have any questions or video requests!

    • @mfonpeter124
      @mfonpeter124 10 หลายเดือนก่อน

      Will it be possible to create lectures on Topology in Real Numbers with n dimensions😣. @@WrathofMath

  • @shahriarjami
    @shahriarjami ปีที่แล้ว +1

    Thank you. it was great❤‍🔥

    • @WrathofMath
      @WrathofMath  ปีที่แล้ว

      Glad to help - thanks for watching!