以下是我尝试运行的代码:
\documentclass{article}
\usepackage{enumerate}
\begin{document}
\begin{enumerate}[label={\alph*)}]
\item Let $\langle a_i \rangle$ and $\langle b_j \rangle$ generate $A, B$. Then $p\in V(A\cap B)$ iff $f(p) = 0$ for all $f \in \langle a_ib_j \rangle$ iff $p\in V(\langle a_i \rangle ) \cup V(\langle b_j \rangle)$. Similarily, $p \in V(A+B)$ iff $p \in V(\langle a_1,\cdots, a_n, b_1, \cdots, b_m \rangle) = V(A) \cap V(B)$.
\item Suppose $f \in I(X \cup Y)$. Then $f$ is $0$ on $X$ and $Y$ so $f\in I(X) \cap I(Y)$. If $f$ is $0$ on $X$ and $Y$ then $f \in I(X \cup Y)$. Any $f \in I(X\cap Y) $ iff $f(X\cap Y) = 0$ iff $f(V(I(X))\cap V(I(Y))) = 0$ iff $f(V(I(X)+I(Y))) = 0 $ iff $f\in I(V(I(X)+I(Y)))$. This gives what was wanted.
\item Note that $I(X) +I(Y) = \langle y \rangle + \langle y -x^2 \rangle = \langle y, x^2 \rangle$ while $I(X \cap Y) = I(V(y,y-x^2)) = I((0,0))$. Clearly $I(X) +I(Y) \subset I((0,0))$ but $x \in I(0,0)$ and $x \notin I(X) +I(Y)$. The desired conclusion follows.
\end{enumerate}
\end{document}
我得到的输出标签如下:
标签=)
磅=)
lcbel=)
在编译过程中,我收到一条错误信息:“缺少数字,视为零”。这是怎么回事?我知道我的 texSettings 文件中有 \usepackage{enumerate}。