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!
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.
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!
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.
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!
Thank you... You've explained it brilliantly!
Thank you!
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.
Again, explaining everything perfectly. Thankyou!
Glad it was helpful!
great example. Thank you!
You are welcome!
Thank you! Great explanation.
np:)
how you choose epsilon/2
Could you apply the same method if the sequence was 1+(1/n)?
Yup
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!!
@@149carmelita the 1 s cancel when u subtract
isn't it enough to show the sequence is convergent
yup it is! I just wanted to do a video using the definition of cauchy:)
Thank you sir
Hey np so glad this helped someone!!
Is -1/n a cauchy sequence and if so can it be rigorously proved?
yea ofc. try it using exact same method
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!
why do we plus 1/N TWICE
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.
I think you haven't noticed that for every epsilon that works and then you can use an arbitrary epsilon.
What? You really are confused.
I/2^n plz solve this problem
what about 1/n! ?
I'd also like to know this.