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    Member kezman's Avatar
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    limit

    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
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    Quote Originally Posted by kezman View Post
    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<q_n<z so that,
    |z-q_n| < \frac{1}{n}.
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