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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@@ -39,7 +39,7 @@ This implies $(m+1)x>\alpha$
Since $(m+1)x\in \alpha$, this contradicts the fact that $\alpha$ is an upper bound of $A$.
EOP
QED
### $\mathbb{Q}$ is dense in $\mathbb{R}$
@@ -59,7 +59,7 @@ By Archimedean property, $\exist n\in \mathbb{N}$ such that $n(y-x)>1$, and $\ex
So $-m_2<nx<m_1$. Thus $\exist m\in \mathbb{Z}$ such that $m-1\leq nx<m$ (Here we use a property of $\mathbb{Z}$) We have $ny>1+nx\geq 1+(m-1)=m$
EOP
QED
### $\sqrt{2}\in \mathbb{R}$, $(\sqrt[n]{x}\in\mathbb{R})$