使用集合的并集和交集将环境与方程对齐时出错

Question

我尝试使用对齐环境来得到以下等式，但没有成功：

有人能帮帮我吗？这是我的代码，但我总是收到错误消息"Extra }, or forgotten \right"

\begin{align}\label{eq18}
  &\left\{N_{A_{1},1} = n_{1},\hdots,N_{A_{1},m}=n_{m} \right\} =  \\
  &\left\{\cup_{b_{1} \in A_{1}(1)} \cup_{a_{2} \in A_{2}(2)} \cdots &\cup_{b_{m} \in A_{1}(m)} \cup_{a_{m+1} \in A_{2}(m+1)}  \nonumber \\
  &\left\{\cap_{i=1}^{m}\left\{N_{A_{1}(i)} = n_{1},X_{K_{i}} = b_{i}, X_{K_{i}+1} = a_{i+1} \right\} \right\} \right\} \cup \nonumber \\
  &\left\{ \cup_{b_{1} \in A_{1}(1)} \cup_{a_{2} \in A_{2}(2)} \cdots &\cup_{a_{m} \in A_{2}(m)} \cup_{b_{m} \in A_{1}(m)}  \nonumber \\
  &\left\{ &\cap_{i=1}^{m-1} \left\{N_{A_{1}(i)} = n_{1},X_{K_{i}} = b_{i}, X_{K_{i}+1} = a_{i+1} \right\}  \cap \nonumber \\
  &\left\{N_{A_{1}(m)} = n_{m}, X_{K_{m}} = b_{m}, X_{K_{m} + 1} = \omega \right\} \right\} \right\}.
\end{align}

Answer 1

这是一个开始...

正如我在评论中指出的那样，

1. 首先，\left{应该是\left\{。对于 也是如此\right}。但是，对于这个解决方案，即使那些也行不通...请参阅 #2。

2. \left...\right不能跨多行拆分。\biggl...\biggr例如，用作替代。

3. 您对换行符\\和列分隔符的使用&需要改进。

MWE。建议您将源代码格式化得更清晰，使用&和\\作为自然断点。这会使调试更容易。

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\label{eq18} \{N_{A_{1},1} = n_{1},\hdots&
  ,N_{A_{1},m}=n_{m} \} = \\ 
&\biggl\{\cup_{b_{1} \in A_{1}(1)} \cup_{a_{2} \in A_{2}(2)} \cdots 
  \cup_{b_{m} \in A_{1}(m)} \cup_{a_{m+1} \in A_{2}(m+1)} \nonumber \\ 
&\biggl\{\cap_{i=1}^{m}\biggl\{N_{A_{1}(i)} = n_{1},X_{K_{i}} = b_{i},
  X_{K_{i}+1} = a_{i+1} \biggr\} \biggr\} \biggr\} \cup \nonumber \\ 
&\biggl\{ \cup_{b_{1} \in A_{1}(1)} \cup_{a_{2} \in A_{2}(2)} \cdots
  \cup_{a_{m} \in A_{2}(m)} \cup_{b_{m} \in A_{1}(m)} \nonumber \\
& \biggl\{ \cap_{i=1}^{m-1} \biggl\{N_{A_{1}(i)} = n_{1},X_{K_{i}} = 
  b_{i}, X_{K_{i}+1} = a_{i+1} \biggr\} \cap \nonumber \\ 
&\biggl\{N_{A_{1}(m)} = n_{m}, X_{K_{m}} = b_{m}, X_{K_{m} + 1} = 
  \omega \biggr\} \biggr\} \biggr\}. 
\end{align}
\end{document}