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**Danneedshelp** How do I prove the following claim?

"Given any $\displaystyle y\in\mathbb{R}$, there exists a sequence of rational numbers that converges to $\displaystyle y$"

I'd assume, I would need to use the fact that Q is dense in R (not the topological version I'm trying to prove) and that, given any epsilon neighborhood around some real number x, I can find a rational number in the interval. I just need help formalizing these thoughts and constructing a solid proof.

Thanks