Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

experimentX Group Title

Balzano-Weirerstrass Theorem: Does any one know why there is \( 2^{m-2} \) at the \( \mathbb{R^n} \) while there is \( 2^{m-1} \) on \( \mathbb{R}^1 \)? http://i.stack.imgur.com/O14VI.jpg

  • one year ago
  • one year ago

  • This Question is Closed
  1. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \( 2^{n-1} \) the the fifth line from proof while \( 2^{m-2} \) on the right bottom

    • one year ago
  2. waterineyes Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait for @mukushla Ha ha ha ha..

    • one year ago
  3. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @experimentX: Apostol?

    • one year ago
  4. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes!! page no 55

    • one year ago
  5. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Which Apostol is it?

    • one year ago
  6. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Tom M. Apostle Mathematical Analysis Second Edition

    • one year ago
  7. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I see.

    • one year ago
  8. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It looks like its because of the way they labeled the subintervals in their proof. In the one dimensional case, they didnt label the starting interval (the one of length 2a, [-a,a]), while in the n-dimensional case they did (J_1 is the n-dimensional rectangle with sides [-a,a]).

    • one year ago
  9. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the first interval is labelled as [a1,b1] which is [-a, 0] or the other, and it's length is 'a' if we continue this we, we get [an, bn] = a/2^(n-1) for the case of R^1

    • one year ago
  10. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    right, but in the n dimensional case, the intervals in J_1 have length 2a.

    • one year ago
  11. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Am I the only idiot here?

    • one year ago
  12. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    J_1 is defined as \( I_1^{(1)} \times I_2^{(1)} \times I_3^{(1)} \times ... I_n^{(1)}\) where each \( I_k^{(1)}: -a \le x \le 0 \)

    • one year ago
  13. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • one year ago
    1 Attachment
  14. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[-a\le x_k\le a\]

    • one year ago
  15. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i see i had been looking at the other page.

    • one year ago
  16. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah, its a little confusing >.<

    • one year ago
  17. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks for clearing up!!

    • one year ago
  18. waterineyes Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @ParthKohli , No you are not alone here..

    • one year ago
  19. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    lol

    • one year ago
  20. waterineyes Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ha ha ha ha.. Even you know about Apostle.. I have heard the word first time in my Life..

    • one year ago
  21. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    He's just an author yaar

    • one year ago
  22. waterineyes Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ha ha ha... I think that is certain set in Mathematics which is given that name.. Ha ha ha. So, I am more Idiot than you..

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.