diff --git a/equivariant_jiang_su_stability_v2.txt b/equivariant_jiang_su_stability_v2.txt
index 29a94b8..c5fe717 100644
--- a/equivariant_jiang_su_stability_v2.txt
+++ b/equivariant_jiang_su_stability_v2.txt
@@ -92,7 +92,7 @@ uniform tracial ultrapower
 
  A^omega = ell^∞(N, A) / I_omega,  I_omega = {(a_j) : lim_{j to omega} |a_j|_{2,u} = 0}. 
 
-The inequalities |ab|_{2,u} le |a| |b|_{2,u} and
+The ineualities |ab|_{2,u} le |a| |b|_{2,u} and
 |ba|_{2,u} le |a| |b|_{2,u} show that I_omega is a closed
 two-sided ideal, and faithfulness of traces embeds A as the constant
 sequences. For any sequence (tau_j) in T(A) the formula
@@ -372,7 +372,7 @@ gives a_{jj} + b_{jj} ge |a_{jj} - b_{jj}| = |d_j| by positivity, so
 
 The operator u is a contraction, so trace-norm duality gives
 Tr(u(a^2 - b^2)) le Tr|a^2 - b^2|. The two
-inequalities prove the lemma.
+ineualities prove the lemma.
 
 Lemma. Let W be a standard Gaussian vector in a finite-dimensional real
 Euclidean space and let B be a real symmetric operator there. Put
@@ -504,7 +504,7 @@ prescription in C:
 
  widetilde Q_{N,E} = sum_{r=1}^D (c_r)/(n^r) sum_{g_1, ..., g_r in E} k_{N;g_1,g_2} ... k_{N;g_{r-1},g_r} (z_{N,g_1} z_{N,g_r} - k_{N;g_r,g_1}), 
 
- Q_{N,E} = tfrac12(widetilde Q_{N,E} + widetilde Q_{N,E}^{,*}). 
+ Q_{N,E} = 1/2(widetilde Q_{N,E} + widetilde Q_{N,E}^{,*}). 
 
 Multiplication is in the displayed order. The empirical covariance array
 need satisfy no positivity condition, because this is a finite polynomial in
@@ -544,7 +544,7 @@ differentiation gives
  (d)/(ds)(e^{i(1-s)tX} e^{istY}) = e^{i(1-s)tX}, it(Y - X), e^{istY}, 
 
 and the tracial 2-seminorm is unchanged by left and right unitary
-multiplication, so integration and the triangle inequality give the
+multiplication, so integration and the triangle ineuality give the
 tracial Duhamel bound |e^{itX} - e^{itY}|_{2,phi} le t|X - Y|_{2,phi}.
 Together with exact equivariance, the norm limit, and the Gaussian
 translation bound, every sequence of traces and indices with convergent
@@ -596,7 +596,7 @@ ultralimit bounds.
 Proof. Every sequence of traces gives the upper bound in each identity.
 Conversely, for each j choose sigma_j in T(A) within 1/j of
 the supremum for the test in question. Its limit trace realizes the reverse
-inequality, since square roots and absolute values commute with ultralimits
+ineuality, since square roots and absolute values commute with ultralimits
 of bounded scalar sequences. For finitely many tests, the coordinates
 satisfying each individual bound with positive slack form a set in
 omega; their intersection is again in omega, hence nonempty and
@@ -678,7 +678,7 @@ f_i^{(r)} : T to [0,1] with
 
 for instance by replacing each indicator near its two endpoints by linear
 ramps whose total lengths tend to zero. Fix r and write f_i = f_i^{(r)},
-e = e_r. Pointwise bounds and the triangle inequality give
+e = e_r. Pointwise bounds and the triangle ineuality give
 
  |f_i^2 - f_i|_{L^2(mu)} le e,  |f_i f_j|_{L^2(mu)} le 2e   (i ne j), 
 
@@ -688,7 +688,7 @@ The first uses |f_i^2 - f_i| le |f_i - chi_i| almost everywhere; the
 second expands
 f_i f_j - chi_i chi_j = (f_i - chi_i) f_j + chi_i (f_j - chi_j) and
 uses chi_i chi_j = 0 almost everywhere; the remaining ones follow from
-sum_i chi_i = 1 almost everywhere and the L^1-L^2 inequality for a
+sum_i chi_i = 1 almost everywhere and the L^1-L^2 ineuality for a
 probability measure.
 
 Set y_i^{(r)} = f_i^{(r)}(w). These are central, invariant positive