Polished A-A and added new lines for broken enumerates.
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Compile Project / Compile (push) Failing after 12s

This commit is contained in:
Bokuan Li
2026-05-05 01:50:35 -04:00
parent 47a7e1de68
commit 0f2e69d1f9
81 changed files with 441 additions and 185 deletions

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@@ -7,7 +7,8 @@
\begin{enumerate}
\item[(LO1)] For any $x, y, z \in E$ with $x \le y$, $x + z \le y + z$.
\item[(LO2)] For any $x, y \in E$ and $\lambda > 0$, $x \le y$ implies that $\lambda x \le \lambda y$.
\end{enumerate}
\end\{enumerate\}
\end{definition}
@@ -17,7 +18,8 @@
\begin{enumerate}
\item $\sup(A + B) = \sup(A) + \sup(B)$.
\item $\sup(A) = -\inf (-A)$
\end{enumerate}
\end\{enumerate\}
\end{proposition}
\begin{proof}
@@ -103,12 +105,14 @@
\begin{enumerate}
\item[(3)] $|\lambda x| = |\lambda| \cdot |x|$
\item[(4)] $|x + y| \le |x| + |y|$.
\end{enumerate}
\end\{enumerate\}
Finally, for any $x, y \in E$ with $x, y \ge 0$,
\begin{enumerate}
\item[(5)] $[0, x] + [0, y] = [0, x + y]$.
\end{enumerate}
\end\{enumerate\}
\end{proposition}
\begin{proof}
@@ -175,7 +179,8 @@
\begin{enumerate}
\item For any $x \in C$ and $\lambda \in \real$ with $\lambda \ge 0$, $\phi(\lambda x) = \lambda \phi(x)$.
\item For any $x, y \in C$, $\phi(x + y) = \phi(x) + \phi(y)$.
\end{enumerate}
\end\{enumerate\}
then the mapping
\[
@@ -218,7 +223,8 @@
\[
|\phi|(x) = \sup\bracs{\phi(y)|y \in E, |y| \le x}
\]
\end{enumerate}
\end\{enumerate\}
\end{proposition}
\begin{proof}