josia-notes/w23-logic-3
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fixed typo
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Josia Pietsch 2024-01-16 12:07:34 +01:00
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inputs/lecture_22.tex
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@ -181,8 +181,8 @@ For this we define
&&\text{then there are $k_m$, $k_n$, $\overline{z}$ such that}\\ &&\text{then there are $k_m$, $k_n$, $\overline{z}$ such that}\\
&&\pi_j(\overline{x_n}) = \pi_j(\overline{z}), \forall k> j+1.~z_k = 1,\\ &&\pi_j(\overline{x_n}) = \pi_j(\overline{z}), \forall k> j+1.~z_k = 1,\\
&&d(f^{k_m}(\overline{x_m}), f^{k_m}(\overline{z})) < \epsilon \text{ and }\\ &&d(f^{k_m}(\overline{x_m}), f^{k_m}(\overline{z})) < \epsilon \text{ and }\\
&&d(f^{k_n}(\overline{x_n}), f^{k_n}(\overline{z})) < \epsilon &&d(f^{k_n}(\overline{x_n}), f^{k_n}(\overline{z})) < \epsilon\\
&&\} &&\}
\end{IEEEeqnarray*} \end{IEEEeqnarray*}
Beleznay and Foreman show that this is open and dense.% Beleznay and Foreman show that this is open and dense.%
\footnote{This is not relevant for the exam.} \footnote{This is not relevant for the exam.}