diff --git a/documents/by-course/math-8/course-notes/main.typ b/documents/by-course/math-8/course-notes/main.typ
index 27e5adf..316c6ac 100644
--- a/documents/by-course/math-8/course-notes/main.typ
+++ b/documents/by-course/math-8/course-notes/main.typ
@@ -25,7 +25,7 @@ competition mathematics or proofs. If you are at UCSB, I highly recommend you
 take this course as soon as possible to unlock the rest of the higher
 mathematics offerings here (which are much more interesting).
 
-= Course Logistics
+= Course logistics
 
 Everything in this section is information only valid for the Winter 2025 quarter with Professor Porter.
 
@@ -457,7 +457,7 @@ $ exists x in U, P(x) $
   We want $1/n < 0.02$, so the idea is to play around with this statement. Taking reciprocals,
   $ n > 50 $
   #proof[
-    Let $N = 50$. Then $n in NN$ and $n > N = 50$,
+    Let $N = 50$. Then $forall n in NN$ and $n > N$,
     $ 1 / n < 1 / 50 = 0.02 $
   ]
 ]