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