diff --git a/metric_entropy_duality_counterexamples_v2.txt b/metric_entropy_duality_counterexamples_v2.txt
index 75fb600..a8b7c09 100644
--- a/metric_entropy_duality_counterexamples_v2.txt
+++ b/metric_entropy_duality_counterexamples_v2.txt
@@ -186,7 +186,7 @@ labels of a partition, never on the size of the underlying set.
 Setup for compression. Let X be a finite nonempty set, let u and q be positive
 integers, and let L_i : X -> Sigma_i, i in [u], be partitions with
 |L_i(X)| <= q. Fix 0 < theta < 1 and a nonempty family Tcal of subsets of [u]
-with |[u] \ T| <= theta u for every T in Tcal; call such T admissible. For
+with |[u] ∖ T| <= theta u for every T in Tcal; call such T admissible. For
 T in Tcal form the undirected graph on X in which distinct x, z are adjacent
 when L_i(x) = L_i(z) for some i in T, and let d_T be its graph distance, with
 d_T = infinity between distinct components. Fix a positive integer h with
@@ -239,7 +239,7 @@ of Y.
 
 A common index. Averaging the admissibility over i,
        (1/u) sum_{i=1}^u mu{(v,T) : i not in T}
-         = sum_{(v,T) in Y} mu_{(v,T)} |[u] \ T|/u <= theta.
+         = sum_{(v,T) in Y} mu_{(v,T)} |[u] ∖ T|/u <= theta.
 So some i_0 in [u] has mu{(v,T) : i_0 not in T} <= theta. Keep the columns in
 Y_0 = {(v,T) in Y : i_0 in T}; the discarded mass is at most theta. This i_0
 serves at every level.
@@ -250,7 +250,7 @@ union, repeatedly add some I_z whose mass outside the current union exceeds
 theta. If k_j sets are added, the successive contributions each exceed
 theta and are disjoint from the previous union, so k_j theta < 1 and
 k_j <= s. The process stops at pivots z_{j,1}, ..., z_{j,k_j} with union
-U_j = union_{k=1}^{k_j} I_{z_{j,k}} such that mu(I_x \ U_j) <= theta for
+U_j = union_{k=1}^{k_j} I_{z_{j,k}} such that mu(I_x ∖ U_j) <= theta for
 every x; the empty case k_j = 0 is allowed. Assign each column of U_j to the
 first pivot whose set contains it, with slot kappa_j(y) in {1, ..., k_j}.
 
@@ -265,7 +265,7 @@ respective hypotheses, even when the graph is disconnected. Define
 and for comparison f_{mu,j}(x) = sum_{y=(v,T) in Y} mu_y * 1{d_T(x,v) <= j}.
 By the forward implication A_j counts every column that f_{mu,j} counts and
 lies in U_j; the remaining columns of f_{mu,j}, either outside Y_0 or in
-I_x \ U_j, carry total mass at most 2 theta. By the backward implication A_j
+I_x ∖ U_j, carry total mass at most 2 theta. By the backward implication A_j
 counts only columns with d_T(x,v) <= 3j + 2. Therefore
        f_{mu,j}(x) - 2 theta <= A_j(x)
          <= sum_{y=(v,T) in Y} mu_y * 1{d_T(x,v) <= 3j + 2}.
@@ -358,7 +358,7 @@ set on the logarithmic scale.
    Robust-directions proposition. Let 0 < theta < 1 and r, h >= 1. Put
    w = 2 D_h and u = ceil(h w/theta), and let p be a prime with
    p > max{h, h^2 u^{2h}}. There exist t_1, ..., t_u in E = F_p^r such that,
-   for every nonzero Z in Sym^h(E^*), some T subset [u] with |[u] \ T| <=
+   for every nonzero Z in Sym^h(E^*), some T subset [u] with |[u] ∖ T| <=
    theta u satisfies Z(t_{i_1}, ..., t_{i_h}) != 0 for every (i_1, ..., i_h) in
    T^h; tuples may repeat indices.
 
@@ -396,7 +396,7 @@ for which this event fails.
 For each nonzero Z take a family of zero tuples with pairwise disjoint supports
 that is maximal under inclusion; it has at most w - 1 tuples. Delete the union
 of the supports and let T be the remaining indices. The number deleted is at
-most h(w-1) < h w <= theta u, so |[u] \ T| <= theta u. If a zero tuple were
+most h(w-1) < h w <= theta u, so |[u] ∖ T| <= theta u. If a zero tuple were
 supported in T, its support would be disjoint from all the chosen ones,
 contradicting maximality. Hence Z is nonzero on every tuple from T^h, and T is
 nonempty because theta < 1. No sampled vector was required to be distinct or
@@ -404,7 +404,7 @@ nonzero.
 
    Separated-rows proposition. With the parameters and directions of the
    robust-directions proposition, set X = Sym^h(E^*), the label map
-   L_i(x) = x(t_i, ., ..., .), and Tcal = {T subset [u] : |[u] \ T| <= theta u}.
+   L_i(x) = x(t_i, ., ..., .), and Tcal = {T subset [u] : |[u] ∖ T| <= theta u}.
    Then |X| = p^{D_h}, each L_i has at most q = p^{D_{h-1}} labels, and for
    every distinct x, y in X there is T in Tcal with d_T(x, y) > h.
    Consequently, with Y = X x Tcal and R_x = (g_{(v,T)}(x))_{(v,T) in Y} in
@@ -451,7 +451,7 @@ order of dependence so the field size can absorb the encoding term.
    separated-rows proposition. The row set is X = Sym^h(F_p^r) with
    m = |X| = p^{D_h} > 1, each label map has at most q = p^{D_{h-1}} labels,
    the columns are indexed by Y = X x Tcal with Tcal = {T subset [u] :
-   |[u]\T| <= theta u}, and the real row vectors obey
+   |[u]∖T| <= theta u}, and the real row vectors obey
    ||R_x - R_{x'}||_{infty,Y} = 1 for distinct x, x'. The set Y is finite and
    nonempty, and the finite field serves only to build the index and label sets;
    the matrix entries and the bodies below are real.