Prove that for every $\displaystyle x \in \mathbb{R}$ exists a secuence $\displaystyle {({q}_{n})}_{n \in \mathbb{N}}$ $\displaystyle \subset \mathbb{Q}$ strictly decreasing so that $\displaystyle \lim_{n \to \infty}q_n = x$
Prove that for every $\displaystyle x \in \mathbb{R}$ exists a secuence $\displaystyle {({q}_{n})}_{n \in \mathbb{N}}$ $\displaystyle \subset \mathbb{Q}$ strictly decreasing so that $\displaystyle \lim_{n \to \infty}q_n = x$
Say, $\displaystyle x>0$ without lose of generality.
Find $\displaystyle 0<q_n<z$ so that,
$\displaystyle |z-q_n| < \frac{1}{n}$.