diff --git a/Advanced/Nonstandard Analysis/parts/1 extensions.tex b/Advanced/Nonstandard Analysis/parts/1 extensions.tex index 1df2389..8f8933c 100644 --- a/Advanced/Nonstandard Analysis/parts/1 extensions.tex +++ b/Advanced/Nonstandard Analysis/parts/1 extensions.tex @@ -51,13 +51,6 @@ An ordered field must satisfy the following properties: \definition{} An ordered field that contains $\mathbb{R}$ is called a \textit{nonarchimedian extension} of $\mathbb{R}$. -\vfill -\pagebreak - - - - - \problem{} Show that each of the following is true in any ordered field. \begin{enumerate} @@ -68,15 +61,14 @@ Show that each of the following is true in any ordered field. \end{enumerate} -\begin{solution} - \textbf{Part A:} - - We know that $x^{-1} \times (x^{-1})^{-1} = 1$ \par - Thus $x \times (x^{-1} \times (x^{-1})^{-1}) = x \times 1 = x$ \par - We can rewrite this as $(x \times x^{-1}) \times (x^{-1})^{-1} = x$ \par - When then becomes $1 \times (x^{-1})^{-1} = x$ \par - And thus $(x^{-1})^{-1} = x$ -\end{solution} +%\begin{solution} +% \textbf{Part A:} +% We know that $x^{-1} \times (x^{-1})^{-1} = 1$ \par +% Thus $x \times (x^{-1} \times (x^{-1})^{-1}) = x \times 1 = x$ \par +% We can rewrite this as $(x \times x^{-1}) \times (x^{-1})^{-1} = x$ \par +% When then becomes $1 \times (x^{-1})^{-1} = x$ \par +% And thus $(x^{-1})^{-1} = x$ +%\end{solution} \vfill