diff --git a/lattice_covering_n_log_n_v2.txt b/lattice_covering_n_log_n_v2.txt
index ebde565..21bc771 100644
--- a/lattice_covering_n_log_n_v2.txt
+++ b/lattice_covering_n_log_n_v2.txt
@@ -2,8 +2,7 @@
 A SINGLE-LATTICE COVERING BOUND OF ORDER n log n
 =====================================================================
 
-A self-contained rewrite for a curious high-school reader who knows
-a little geometry and a little probability. Everything is stated and
+A self-contained rewrite. Everything is stated and
 then proved. Two deep facts are imported from the literature: the Eldan--Klartag
 marginal theorem and the Rogers--Schmidt mean-hole estimate. Everything
 else, including the Li--Liu binary correction and the completion
@@ -1192,7 +1191,7 @@ expectation <= C' b^{-1/2}; fix that W. Then define
 
 Weighted Markov's inequality gives the explicit discarded mass
 
-    E_z F_b(t_z) ind_{E_b \ U_b}(z)
+    E_z F_b(t_z) ind_{E_b ∖ U_b}(z)
         <= C' b^{-1/2 + 1/20} = C' b^{-9/20}.               (9.12)
 
 Together with (9.2), this proves the third assertion in (9.9):
@@ -2164,7 +2163,7 @@ enough mass. A direct application of Lemma 7.2 (with the "for
 sufficiently large m" form (7.8)) gives one lattice Lambda_h of
 covolume D_h whose hole sets
 
-    U_a = ( R^m / Lambda_h ) \ pi_{Lambda_h}(J_a)
+    U_a = ( R^m / Lambda_h ) ∖ pi_{Lambda_h}(J_a)
 
 satisfy |U_a| <= e^{-u_a/2} simultaneously for all retained labels.
 Thus the horizontal lattice has covered all listed slices up to tiny