The title is self-explanatory. How would I go about proving "$1 \leq x \leq 2$ if and only if $1 \leq x \leq 1 + \frac{1}{n}$ for some $n \in \mathbb{N}$"?
2026-02-23 20:43:48.1771879428
Let $x \in \Bbb{R}$. Prove $1 \leq x \leq 2$ if and only if $1 \leq x \leq 1 + \frac{1}{n}$ for some $n \in \mathbb{N}$?
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Hint:
$2=1+\dfrac{1}{1}$ and $1+\dfrac{1}{n}\leq 2$ for all $n\in\mathbb{N}$.