update notations and fix typos
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@@ -77,7 +77,7 @@ This proves that $\lim_{n\to\infty} |s_n - t_n| = 0$.
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Since $\lim_{n\to\infty} s_n$ exists, $\lim_{n\to\infty} s_n = \lim_{n\to\infty} t_n$.
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EOP
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QED
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#### Theorem 3.54
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@@ -137,7 +137,7 @@ Then: $(p_n)$ is a sequence in $E\backslash\{p\}$ with $d_X(p_n,p) = \frac{1}{n}
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So $\lim_{n\to\infty} f(p_n) \neq q$.
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EOP
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QED
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With this theorem, we can use the properties of limit of sequences to study limits of functions.
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