diff --git a/nearby_lagrangian_counterexample_v2.txt b/nearby_lagrangian_counterexample_v2.txt
index e80aaec..3bc2543 100644
--- a/nearby_lagrangian_counterexample_v2.txt
+++ b/nearby_lagrangian_counterexample_v2.txt
@@ -1153,7 +1153,7 @@ SECTION 5. THE ZERO-LEVEL COBORDISM ARGUMENT
 
     which is a homotopy equivalence. It identifies C_b with
 
-        T_{-,b}^1 \ Int( j_b( T_-^0 ) ).
+        T_{-,b}^1 minus Int( j_b( T_-^0 ) ).
 
     In particular C_b, with its fixed incoming identification with Sigma, is
     a smooth family of h-cobordisms.
@@ -1255,7 +1255,7 @@ SECTION 5. THE ZERO-LEVEL COBORDISM ARGUMENT
 
     Extension. If e: X -> Y is a codimension-zero embedding, the extension
     e_!: H(X) -> H(Y) glues the cobordism to the trivial cylinder on
-    Y \ Int(e(X)) along the product vertical boundary. In the bent collared
+    Y minus Int(e(X)) along the product vertical boundary. In the bent collared
     model this is C |-> (Y x I) union_{X x I} C, where X x I subset C is the
     incoming collar. This expression shows that extension commutes with
     interval stabilization.
@@ -1551,7 +1551,7 @@ SECTION 6. BUILDING THE EXACT EMBEDDED LAGRANGIAN
     neighborhoods of the two critical points of theta on which g_b is the
     fixed quadratic form q_{m,m}. Set
 
-        delta_0 = min over B \ U_0 of |d theta| > 0.
+        delta_0 = min over B minus U_0 of |d theta| > 0.
 
     Section 3.8 gives the mixed derivative bound |d_w d_b g_b(w)| <= C_1 |w|,
     and the two-sided gradient bound c |w| <= |grad_w g_b(w)| <= C |w|.
@@ -1860,7 +1860,7 @@ SECTION 7. HAMILTONIAN TRANSPORT AND THE CONTRADICTION
     This expression vanishes outside the compact mixed-coordinate image of K.
     Its spatial projection lies in a fixed compact subset of U, because both
     the input and output trajectories remain in K. Enlarge that projection
-    slightly to obtain D contained in U. So for every X in U \ D, sigma and all
+    slightly to obtain D contained in U. So for every X in U minus D, sigma and all
     its derivatives vanish on a neighborhood of X, for all momenta. Finally
     I + sigma_(pX) = D_X x is invertible, and sigma_p = x - X tends uniformly
     to zero as the time increment tends to zero. QED.
@@ -1950,7 +1950,7 @@ SECTION 7. HAMILTONIAN TRANSPORT AND THE CONTRADICTION
     critical point has |w| >= R_o; at every one of them chi = 1 on a
     neighborhood as well.
 
-    There are two open regions, namely V and U \ D; they cover U.
+    There are two open regions, namely V and U minus D; they cover U.
 
     Region X in V: the three cutoff factors are 1 near a solution, and the
     critical equations become
@@ -1970,7 +1970,7 @@ SECTION 7. HAMILTONIAN TRANSPORT AND THE CONTRADICTION
     I + sigma_(pX) in X. This triangular order proves surjectivity of the
     differential of the full new vertical-gradient map.
 
-    Region X in U \ D: the function sigma vanishes on a spatial neighborhood
+    Region X in U minus D: the function sigma vanishes on a spatial neighborhood
     for all p. The equations instead reduce to
 
         (7.16)  z = 0,  x = X,  grad_w F_o(X,w) = 0,