Fix typos
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2025-01-19 20:24:51 -08:00
parent cb2a1d99dd
commit 5f8c54650f
30 changed files with 105 additions and 49 deletions

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@ -52,7 +52,7 @@ An ordered field must satisfy the following properties:
An ordered field that contains $\mathbb{R}$ is called an \textit{extension} of $\mathbb{R}$.
\definition{}
The \textit{Archimedian property} states the following: \par
The \textit{Archimedean property} states the following: \par
For all positive $x, y$, there exists an $n$ so that $nx \geq y$.
\theorem{}
@ -149,7 +149,9 @@ In an ordered field, the \textit{magnitude} of a number x is defined as follows:
\end{equation*}
\definition{}
We say an element $\delta$ of an ordered field is \textit{infinitesimal} if $|nd| < 1$ for all $n \in \mathbb{Z^+}$. \par
We say an element $\delta$ of an ordered field is \textit{infinitesimal} if
$|nd| < 1$ % spell:disable-line
for all $n \in \mathbb{Z^+}$. \par
\note{Note that $\mathbb{Z}^+$ is a subset of any nonarchimedian extension of $\mathbb{R}$.} \par
\vspace{2mm}