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Typo fix.
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Bokuan Li
2026-03-12 22:36:53 -04:00
parent 532bced3b7
commit 6bb13c3c53
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src/fa/lc/inductive.tex
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@@ -174,7 +174,7 @@
\end{itemize} \end{itemize}
In which case, since $U_{k} \supset U_{k+1}$ for all $k \in \natp$, In which case, since $U_{k} \supset U_{k+1}$ for all $k \in \natp$,
\[ \[
\underbracs{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n} \underbrace{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n}
\] \]
which is impossible. Therefore $(F_n + U) \cap E_n = \emptyset$ for all $n \in \natp$. which is impossible. Therefore $(F_n + U) \cap E_n = \emptyset$ for all $n \in \natp$.