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Zheyuan Wu
2024-12-08 14:38:45 -06:00
parent f5f0e2a5c3
commit 6ffcf9e50d
2 changed files with 2 additions and 2 deletions
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pages/Math4111/Math4111_L3.md
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@@ -122,4 +122,4 @@ We define $\mathbb{R}$ to be the unique ordered field with $LUBP$. (The existenc
#### Theorem 1.20 #### Theorem 1.20
1. (Archimedean property) If $x,y\in \mathbb{R}$ and $x>0$, then $\exists n\in \mathbb{N}$ such that $nx>y$. 1. (Archimedean property) If $x,y\in \mathbb{R}$ and $x>0$, then $\exists n\in \mathbb{N}$ such that $nx>y$.
2. ($\mathbb{Q}$ is dense in $\mathbb{R}$) If $x,y\in \mathbb{R}$ and $x<y$, then $\exists p\in \mathbb{Q}$$ such that $x<p<y$. 2. ($\mathbb{Q}$ is dense in $\mathbb{R}$) If $x,y\in \mathbb{R}$ and $x<y$, then $\exists p\in \mathbb{Q}$ such that $x<p<y$.

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pages/Math4111/Math4111_L4.md
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@@ -43,7 +43,7 @@ EOP
### $\mathbb{Q}$ is dense in $\mathbb{R}$ ### $\mathbb{Q}$ is dense in $\mathbb{R}$
$\mathbb{Q}$ is dense in $\mathbb{R}$) If $x,y\in \mathbb{R}$ and $x<y$, then $\exists p\in \mathbb{Q}$$ such that $x<p<y$. $\mathbb{Q}$ is dense in $\mathbb{R}$ if $x,y\in \mathbb{R}$ and $x<y$, then $\exists p\in \mathbb{Q}$ such that $x<p<y$.
Some thoughts: Some thoughts: