Fixed more mistakes in the dyadic rational numbers.
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@@ -44,10 +44,10 @@
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\item[(b)] For each $x, y \in G$, $x + y \ge x, y$.
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\end{enumerate}
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For each $x \in \mathbb{D} \cap [0, 1)$, let $\phi(x) = \sum_{n \in M(x)}g_n$, then
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For each $x \in \mathbb{D} \cap (0, 1)$, let $\phi(x) = \sum_{n \in M(x)}g_n$, then
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\begin{enumerate}
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\item For any $x, y \in \mathbb{D} \cap [0, 1)$ such that $x + y \in [0, 1)$, $\phi(x) + \phi(y) \le \phi(x + y)$.
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\item For any $x, y \in \mathbb{D} \cap [0, 1)$ with $x \le y$, $\phi(x) \le \phi(y)$.
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\item For any $x, y \in \mathbb{D} \cap (0, 1)$ such that $x + y \in (0, 1)$, $\phi(x) + \phi(y) \le \phi(x + y)$.
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\item For any $x, y \in \mathbb{D} \cap (0, 1)$ with $x \le y$, $\phi(x) \le \phi(y)$.
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\end{enumerate}
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\end{proposition}
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\begin{proof}
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