Sequence that has all rational numbers
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! 
Re: Sequence that has all rational numbers
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.

Re: Sequence that has all rational numbers
thanks! can you elaborate a little bit? I'm trying to selfstudy 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! 
Re: Sequence that has all rational numbers
Quote:
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. 
Re: Sequence that has all rational numbers
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! 
Re: Sequence that has all rational numbers
You might look here for an idea.
http://www.homeschoolmath.net/teachi...countable.php 
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