update notations and fix typos

This commit is contained in:
Zheyuan Wu
2025-02-25 20:41:35 -06:00
parent 419ea07352
commit 27bff83685
71 changed files with 920 additions and 430 deletions

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