Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequence that has all rational numbers

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Construct a sequence that has all rational numbers in it

    2. Relevant equations

    None.

    3. The attempt at a solution

    Here are my thoughts, though I have no solutions yet.

    If I construct a sequence Sn= n*sin(n)-1/n, will it work?

    Thanks guys!
     
  2. jcsd
  3. Jan 26, 2012 #2
    The sine term will often give irrational numbers, so that won't work. Try putting the rationals in an array and finding a path that goes through all of them.
     
  4. Jan 26, 2012 #3
    thanks! can you elaborate a little bit? I'm trying to self-study real analysis, and I'm not really familiar with what you just mentioned...
    how would i put them in an array and find a "path"?

    thanks!
     
  5. Jan 26, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Just drop the sine term.

    OR

    Do you really want a sequence with all of the rational numbers in it. -- maybe just all of the positive rationals?

    Better yet: Please type the problem word fro word as it was presented to you.
     
  6. Jan 26, 2012 #5
    Hi guys:

    Thank you so much! Here's the problem as it was typed on the book:

    Construct a sequence such that every real number is its limit point.

    I know this is different from the question I typed above, but my reasoning is that if i can have a sequence that contains all rational numbers, then I can prove that every real number is its limit point. Does that make sense? How should I solve the original question if this does not?

    Thank you!
     
  7. Jan 26, 2012 #6

    LCKurtz

    User Avatar
    Homework Helper
    Gold Member

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?