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