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Simple Rudin

  1. Jan 29, 2009 #1
    Hello,

    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]
    Proof:
    Since [itex] x<y[/itex], we have [itex] y-x>0[/itex] and the Archemedian Property furnishes a positive integer n such that:
    [itex]n(y-x)>1[/itex]
    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
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