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Math Help - About accumulation points of a set in [0,1]

  1. #1
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    About accumulation points of a set in [0,1]

    Hi!


    If \lambda>0:
    What are the accumulation points of A=\left\{\lambda n-[\lambda n]:n\in\mathbb{N}\right\} in [0,1]?


    Thanks in advance!
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  2. #2
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    Re: About accumulation points of a set in [0,1]

    Is [\lambda n] the floor function?
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  3. #3
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    Re: About accumulation points of a set in [0,1]

    Quote Originally Posted by Gusbob View Post
    Is [\lambda n] the floor function?
    Yes.
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  4. #4
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    Re: About accumulation points of a set in [0,1]

    Quote Originally Posted by Gusbob View Post
    Is [\lambda n] the floor function?
    It far more than that. Look at the webpage.


    Quote Originally Posted by eraldcoil View Post
    If \lambda>0:
    What are the accumulation points of A=\left\{\lambda n-[\lambda n]:n\in\mathbb{N}\right\} in [0,1]?
    Well at least I have no worry that Soroban will give a complete solution to this one.

    This is a great teaching question. DO IT!

    First let \lambda =\tfrac{1}{2} then \lambda =\tfrac{1}{4} then \lambda =\tfrac{3}{5}.

    Now what happens if \lambda =\tfrac{\pi}{2}~?

    If you go back to that webpage, look at the graphs, what is going on?
    Thanks from Gusbob and HallsofIvy
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