Will every rational number eventually be in this set? – math.stackexchange.com

Let $A_0=\{0\}$. For every $n\ge 0$, let $B_n=\bigcup_{k\ge 0}A_n+k$, and let $A_{n+1}=f(B_n)$, where $f:[0,\infty)\to[0,1):x\mapsto\frac{x}{x+1}$. Let $q\in\Bbb Q\cap [0,1)$. Can we prove that $q\in ...

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