diff --git a/inputs/lecture_03.tex b/inputs/lecture_03.tex
index 170dbed..06256d1 100644
--- a/inputs/lecture_03.tex
+++ b/inputs/lecture_03.tex
@@ -64,7 +64,7 @@ all condensation points are accumulation points.
         For $\supseteq$ let $y$ be an element of the RHS.
         Then $y \in (a_{x_0}, b_{x_0}) \cap A$ for some $x_0$.
         As $(a_{x_0}, b_{x_0}) \cap A$ is at most countable,
-        $y \in P$.
+        $y \not\in P$.
 
         Now we have that $A \setminus P$ is a union
         of at most countably many sets,
diff --git a/inputs/lecture_14.tex b/inputs/lecture_14.tex
index 6d0297e..9435d2f 100644
--- a/inputs/lecture_14.tex
+++ b/inputs/lecture_14.tex
@@ -125,7 +125,6 @@ We have shown (assuming \AxC to choose contained clubs):
     The \vocab{diagonal intersection},
     is defined to be
     \[
-
     \diagi_{\beta < \alpha} A_{\beta} \coloneqq 
     \{\xi < \alpha : \xi \in \bigcap \{A_{\beta} : \beta < \xi\}  \}.
     \]