diff --git a/critical_ising_stopping_band_v2.txt b/critical_ising_stopping_band_v2.txt
index fd7adf4..f9490c3 100644
--- a/critical_ising_stopping_band_v2.txt
+++ b/critical_ising_stopping_band_v2.txt
@@ -2,9 +2,7 @@
 BUFFERED COMPARISON AND STOPPING-BAND RESOLUTION IN CRITICAL ISING
 ================================================================================
 
-An expository, self-contained version, written to be readable by a
-high-school student who is comfortable with probability and wants to see
-the full argument, with no steps hidden.
+An expository, self-contained version, with no steps hidden.
 
 The original paper is a LaTeX article. Here every theorem, lemma, and
 corollary is restated in plain text and proved. Symbols are kept as in
@@ -910,8 +908,8 @@ inequality in L^4.) Paley-Zygmund gives c_2, p_2 > 0 with
 P(X >= c_2 w^{7/4}) >= p_2.
 
 Let L be the largest number of sites of L_2 lying in one auxiliary
-cluster. Then L^2 <= sum over clusters C of |C\cap L_2|^2 and
-E sum_C |C\cap L_2|^2 = E(sum_{L_2} Y_x)^2 <= C_2 w^{7/4}. Choose K with
+cluster. Then L^2 <= sum over clusters C of |C∩ L_2|^2 and
+E sum_C |C∩ L_2|^2 = E(sum_{L_2} Y_x)^2 <= C_2 w^{7/4}. Choose K with
 C_2/K^2 < p_2/2; then with probability at least p_2/2 both
 X >= c_2 w^{7/4} and L <= K w^{7/8}. Every site of L_1 reaching L_2
 contributes at most L to X, so on that event at least (c_2/K) w^{7/8} sites