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!
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?