I am looking for a sequence with infinitely many limit points. I don't want to use $\log,\sin,\cos$ etc.!
It's easy to find a sequence like above, e.g. $1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,\dots$
But how can you prove the limit points? The problem I am having is the recursion or definiton of the sequence which I can't name exactly. But for a formal proof I need this.
So what's a sequence with infinitely many limit points without using $\log,\sin,\cos$ or any other special functions?