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@ -51,13 +51,6 @@ An ordered field must satisfy the following properties:
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\definition{}
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An ordered field that contains $\mathbb{R}$ is called a \textit{nonarchimedian extension} of $\mathbb{R}$.
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\vfill
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\pagebreak
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\problem{}
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Show that each of the following is true in any ordered field.
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\begin{enumerate}
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@ -68,15 +61,14 @@ Show that each of the following is true in any ordered field.
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\end{enumerate}
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\begin{solution}
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\textbf{Part A:}
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We know that $x^{-1} \times (x^{-1})^{-1} = 1$ \par
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Thus $x \times (x^{-1} \times (x^{-1})^{-1}) = x \times 1 = x$ \par
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We can rewrite this as $(x \times x^{-1}) \times (x^{-1})^{-1} = x$ \par
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When then becomes $1 \times (x^{-1})^{-1} = x$ \par
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And thus $(x^{-1})^{-1} = x$
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\end{solution}
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%\begin{solution}
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% \textbf{Part A:}
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% We know that $x^{-1} \times (x^{-1})^{-1} = 1$ \par
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% Thus $x \times (x^{-1} \times (x^{-1})^{-1}) = x \times 1 = x$ \par
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% We can rewrite this as $(x \times x^{-1}) \times (x^{-1})^{-1} = x$ \par
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% When then becomes $1 \times (x^{-1})^{-1} = x$ \par
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% And thus $(x^{-1})^{-1} = x$
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%\end{solution}
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\vfill
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