So i have the bijection $a:$ $\mathbb {N} \rightarrow \mathbb {Q}$.

I was asked to find the limit points / cluster points of the sequence $a\_n = a(n)$.

I know that this bijection exists since $\mathbb {N}$ and $\mathbb {Q}$ are both countable. After reading up in my script, I know how they constructed it using Cantor's diagonal argument. This is where I'm stuck though, since I just read that apparently this sequence has every real number as a limit point of the sequence. How can this be proven?