Created the Abstract Algebra theorems and definitions cheat sheet

part-5/chapters/chapter-27/isometries.tex

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+\section{Isometries}
+
+\begin{remark}
+	It is convenient to begin our discussion with the definition of an isometry (from the Greek \textit{isometros}, meaning "equal measure") in $\R^n$.
+\end{remark}
+
+\begin{definition}[Isometry]
+	An \textit{isometry} of $n$-dimensional space $\R^n$ is a function from $\R^n$ onto $\R^n$ that preserves distance.
+\end{definition}
+
+\begin{definition}[Symmetry Group of a Figure in $\mathbf{\R^n}$]
+	Let $F$ be a set of points in $\R^n$. the \textit{symmetry group of $F$} in $\R^n$ is the set of all isometries of $\R^n$ that carry $F$ onto itself. The group operation is function composition.
+\end{definition}