Proof that the Sequence {1/n} is a Cauchy Sequence

Поділитися
Вставка
  • Опубліковано 25 гру 2024

КОМЕНТАРІ • 29

  • @dunkelheit3129
    @dunkelheit3129 5 років тому +18

    Still can't believe that in the end I've found someone that explain why we can choose N, for the Archimedean property of real numbers.
    I was wondering for a lot of time why we can make some choices, I always thought it was a big fog behind that process of choice; but you've clarified it to me now and I'm so grateful. Thanks!

  • @geetasingh4746
    @geetasingh4746 5 років тому +3

    Thank you... You've explained it brilliantly!

  • @uzair3690
    @uzair3690 2 роки тому

    Since capital N belongs to the positive integers so i think we should put 2/ε in greatest integer function...right? like this N> [2/ε] where [•] denote greatest integer function.
    Also we should add 1in N>[2/ε]+1 in case ε tends to infinity.

  • @thomasyassmin715
    @thomasyassmin715 4 роки тому +3

    Again, explaining everything perfectly. Thankyou!

  • @nalansipahi-stallmann5263
    @nalansipahi-stallmann5263 3 роки тому +1

    great example. Thank you!

  • @juarjuna4130
    @juarjuna4130 6 років тому +1

    Thank you! Great explanation.

  • @EjazAhmed-pf5tz
    @EjazAhmed-pf5tz 2 роки тому +2

    how you choose epsilon/2

  • @149carmelita
    @149carmelita 5 років тому +2

    Could you apply the same method if the sequence was 1+(1/n)?

    • @TheMathSorcerer
      @TheMathSorcerer  5 років тому

      Yup

    • @149carmelita
      @149carmelita 5 років тому +2

      Also, when we calculate the distance: [Xn-Xm] for the sequence 1+(1/n), do we ignore the 1? and write the distance as [(1/n)-(1/m)]? Thanks!!

    • @TheMathSorcerer
      @TheMathSorcerer  5 років тому +1

      @@149carmelita the 1 s cancel when u subtract

  • @semirumutkurt6635
    @semirumutkurt6635 6 років тому +4

    isn't it enough to show the sequence is convergent

    • @TheMathSorcerer
      @TheMathSorcerer  6 років тому +2

      yup it is! I just wanted to do a video using the definition of cauchy:)

  • @kaiwang8175
    @kaiwang8175 6 років тому +1

    Thank you sir

  • @silversharky3258
    @silversharky3258 5 років тому +1

    Is -1/n a cauchy sequence and if so can it be rigorously proved?

    • @AlexandreLopez1999
      @AlexandreLopez1999 5 років тому +1

      yea ofc. try it using exact same method

    • @joaohax52
      @joaohax52 4 роки тому +1

      this question was released one year ago but.. you can use the same way as the video showed:
      |-1/n -(- 1/m)| = |-1/n + 1/m| = |1/n - 1/m|
      and do the same way!

  • @nichakornprukpaiboon9018
    @nichakornprukpaiboon9018 Рік тому

    why do we plus 1/N TWICE

  • @arghyachakraborty5181
    @arghyachakraborty5181 4 роки тому

    I am confused at a point that a sequence is to be cauchy for all epsilon greater than zero but in this proof we just take an arbitrary epsilon . How this represents all the epsilon please clarify.

    • @joaohax52
      @joaohax52 4 роки тому

      I think you haven't noticed that for every epsilon that works and then you can use an arbitrary epsilon.

    • @samueldeandrade8535
      @samueldeandrade8535 6 місяців тому

      What? You really are confused.

  • @vikash_vlogs826
    @vikash_vlogs826 3 роки тому

    I/2^n plz solve this problem

  • @AlEx-ro7kd
    @AlEx-ro7kd 3 роки тому

    what about 1/n! ?