\begin{definition}
%@see: 《Real Analysis Modern Techniques and Their Applications Second Edition》 P5
设\(\opair{X,\leq},\opair{Y,\preceq}\)都是偏序集.
如果存在一个双射\(f\colon X \to Y\)，
使得\[
	(\forall x_1,x_2 \in X)
	[
		x_1 \leq x_2
		\iff
		f(x_1) \preceq f(x_2)
	],
\]
那么称“\(\opair{X,\leq}\)和\(\opair{X,\preceq}\)
是\DefineConcept{序同构的}（order isomorphic）”.
\end{definition}

\begin{definition}
设\(X\)由\(\leq\)线性排列，
且\(X\)的每个非空子集都存在最小元，
则称“\(X\)由\(\leq\)~\DefineConcept{良好排列}（\(X\) is \emph{well ordered} by \(\leq\)）”，
或称“\(X\)是\DefineConcept{良序集}（well ordered set）”，
称\(\leq\)为“\(X\)上的\DefineConcept{良序}（a \emph{well ordering} on \(X\)）”.
\end{definition}

%@see: 《Real Analysis Modern Techniques and Their Applications Second Edition》 P9





%@see: 《Real Analysis Modern Techniques and Their Applications Second Edition》 P10

\begin{definition}
定义：\[
	\overline{\mathbb{R}}
	\defeq
	\mathbb{R}
	\cup
	\{-\infty,+\infty\}.
\]
将其称为\DefineConcept{扩展实数系}（extended real number system）.
\end{definition}