diff --git a/closed_ricci_flow_curvature_blowup_v2.txt b/closed_ricci_flow_curvature_blowup_v2.txt
index c4091b9..986ce3b 100644
--- a/closed_ricci_flow_curvature_blowup_v2.txt
+++ b/closed_ricci_flow_curvature_blowup_v2.txt
@@ -464,7 +464,7 @@ all. That is why U_k's two asymptotics, one at each end, are stated as part of
 the input.
 
 Item (iii) is the inner region, below Y_1 theta, where the profiles are not
-available. There the assumptions are inequalities instead: the metric is on the
+available. There the assumptions are ineualities instead: the metric is on the
 far side of the cone in the ratio phi/r, the logarithmic slope f lies in [0,1]
 and is monotone, and z is trapped in [B^2,1]. These are exactly what the pole
 size lemma needs. The intervals in (iii) lie strictly below the equator, which
@@ -479,7 +479,7 @@ of Theorem 1.1 of Stolarski's paper. Assembly, source by source:
   weighted profile estimates   Definition 3.1;
   the initial family           Definition 3.5 and Lemma 3.6, with the outer
                                conditions of Definition 3.2;
-  the inner inequalities       Inner Region Barriers I of Definition 3.3, as
+  the inner ineualities       Inner Region Barriers I of Definition 3.3, as
                                propagated by Lemmas 4.5 to 4.9 and explicitly
                                invoked in the proof of Theorem 4.3 on page 25
                                of that paper;
@@ -498,7 +498,7 @@ k, and by Propositions A.10 and A.19 the homogeneous lower Z-modes are gamma^2
 times polynomials with growth exponents strictly below 2k - d. There are only
 finitely many such modes, and each one, together with its first two
 derivatives, is bounded by the corresponding weight in the displayed
-inequalities on all of gamma > 0. Taking the lower-mode coefficient bound at
+ineualities on all of gamma > 0. Taking the lower-mode coefficient bound at
 the initial time to be eps_0 delta^nu with eps_0 small enough gives the needed
 tolerances. This choice is compatible with the degree argument in Lemma 3.10:
 the projection errors in Lemmas 6.13 and 6.14 can be reduced afterwards by
@@ -518,7 +518,7 @@ The source's notation and the notation of this document are related by
 
 Thus the source's moving cutoff, which is a constant times exp(-alpha_k tau)
 in the gamma variable, becomes a constant times theta in the r variable. The
-log-radius convexity condition in the source becomes the slope inequality in
+log-radius convexity condition in the source becomes the slope ineuality in
  (iii) through
 
     f = 1 + gamma Ut_gamma,
@@ -718,7 +718,7 @@ Proof. For 0 < gamma <= 1 the fixed profiles and their errors satisfy
 |Zt| <= C'_{q,k} delta^nu gamma^(-d) above their respective lower cutoffs.
 Enlarge Y_1 and then Y_2 until the right sides at those cutoffs are at most
 1/q; they only decrease as gamma increases, so this suffices for the whole
-range. In the remaining inner range use the inequalities of item (iii). Now
+range. In the remaining inner range use the ineualities of item (iii). Now
 use the three identities
 
     1 - B^2 = 2/(q+1),     r u_r = 1 + gamma Ut_gamma,
@@ -926,7 +926,7 @@ phi_ss/phi, and phi_ss/phi = z (u_rr + u_r^2) + z_r u_r/2 while r_ss = z_r/2;
 substituting u_r = f/r gives the formula.
 
 Suppose the lower bound failed. Take times tending to T for which
-L_0 = phi(0,t) = o(theta). The inequalities r_s >= B and |phi_s| <= C give
+L_0 = phi(0,t) = o(theta). The ineualities r_s >= B and |phi_s| <= C give
 
     phi(L_0,t)/L_0 <= 1 + C/B.
 
@@ -984,7 +984,7 @@ Proof. Put w = 1 - v. The second sideways equation gives
     ( d_t - z d_rr - ((q-1-z)/r) d_r + (q-1) v (1+v)/r^2 ) w
         = p v^3 u_r^2 <= C theta^(-2).
 
-The last inequality uses u_r = phi_s/(phi v), Lemma 6.2, and B <= v <= 1 at
+The last ineuality uses u_r = phi_s/(phi v), Lemma 6.2, and B <= v <= 1 at
 the cap scale. Apply the same operator to r/theta; the result is exactly
 
     sigma r/(delta theta) + [ (q-1)(v(1+v) - 1) + z ] / (r theta).
@@ -1225,7 +1225,7 @@ The tensor evolution, together with the evolution of the metric, gives
     (d_t - Laplacian) |Ric|^2 = -2 |grad Ric|^2 + 4 <Rm(Ric), Ric>,
 
 where the inverse-metric derivatives in the squared norm cancel the cubic Ricci
-term from the covariant evolution of the tensor. Kato's inequality then gives,
+term from the covariant evolution of the tensor. Kato's ineuality then gives,
 wherever |Ric| > 0,
 
     (d_t - Laplacian) |Ric|