Hi!

If $\displaystyle \lambda>0$:

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

Thanks in advance!

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- Apr 11th 2013, 03:32 PMeraldcoilAbout accumulation points of a set in [0,1]
Hi!

If $\displaystyle \lambda>0$:

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

Thanks in advance! - Apr 11th 2013, 04:28 PMGusbobRe: About accumulation points of a set in [0,1]
Is $\displaystyle [\lambda n] $ the floor function?

- Apr 11th 2013, 04:42 PMeraldcoilRe: About accumulation points of a set in [0,1]
- Apr 11th 2013, 05:01 PMPlatoRe: About accumulation points of a set in [0,1]
It far more than that. Look at the webpage.

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 $\displaystyle \lambda =\tfrac{1}{2}$ then $\displaystyle \lambda =\tfrac{1}{4}$ then $\displaystyle \lambda =\tfrac{3}{5}$.

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

If you go back to that webpage, look at the graphs, what is going on?