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$\newcommand{\N}{\mathbb{N}}$ $\newcommand{\set}[1]{\{#1\}}$ For each $n \in \N^+$, let $X_n = \set{0, 2}$. Let $X = \Pi_{n \in \N^+} X_n$. Define a function $f: X \to [0, 1]$ by setting $$f(x) = \sum_{n = 1}^{\infty} \frac{x_n}{3^n}$$. Prove that $f$ is one to one
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Sun, 15 Sep 2019 17:24 GMT