1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Rudin

  1. Jan 29, 2009 #1

    I have decided to study analysis on my own and am starting with principles of mathematical analysis by rudin.
    I am having trouble understanding pg. 9 on the density of Q in R, part b.

    It states:
    If [itex]x \in R, y \in R [/itex] and [itex] x<y [/itex] the there exists a [itex] p \in Q [/itex] such that [itex]x < p < y[/itex]
    Since [itex] x<y[/itex], we have [itex] y-x>0[/itex] and the Archemedian Property furnishes a positive integer n such that:
    Applying the AP again, to obtain positive integers m1 & m2 such that [itex]m1>nx[/itex], [itex]m2>-nx[/itex]
    Then: [itex]-m2<nx<m1 [/itex]
    Hence there is an integer m such that [itex]m-1 \le nx<m [/itex]........

    Can someone explain to me the last line? Where does this less then or equal come from?
  2. jcsd
  3. Jan 30, 2009 #2
  4. Jan 30, 2009 #3
  5. Jan 30, 2009 #4
  6. Jan 31, 2009 #5
    MMmm....For being my first analysis book Principles of Mathematical Analysis by Rudin might be a little too hard. Should I study Apostol's Principles of Mathematical Analysis first? Then go back to Rudin's text?
  7. Jan 31, 2009 #6
    Probably depends how much you already know.
  8. Jan 31, 2009 #7
    Calc 1-3. No analysis experience.
  9. Jan 31, 2009 #8
    Yah i need a text for self study. I have no experience with proofs.
  10. Jan 31, 2009 #9
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Simple Rudin
  1. Rudin 1.21 (Replies: 3)

  2. Rudin Reference (Replies: 8)

  3. Companion for Rudin? (Replies: 1)

  4. Rudin's equation (Replies: 2)