diff --git a/crossing_number_bipartite_v2.txt b/crossing_number_bipartite_v2.txt
index c8fa66c..827507d 100644
--- a/crossing_number_bipartite_v2.txt
+++ b/crossing_number_bipartite_v2.txt
@@ -93,7 +93,7 @@ document gives the exact formula with a complete proof.
 
 3. THE PLAN
 
-3.1  Two inequalities suffice.
+3.1  Two ineualities suffice.
       Upper bound:  cr(K_{m,n}) <= d_m d_n.  Exhibit ONE drawing.
       Lower bound:  cr(K_{m,n}) >= d_m d_n.  Show EVERY drawing crosses
                     at least d_m d_n times.
@@ -111,7 +111,7 @@ the geometry into linear algebra:
       (c) A linear map Phi (called the rank detector) sends each block
           J^{ik} to a matrix  R_ik = X_i - Y_k,  with X_i - Y_i
           invertible.
-      (d) A linear-algebra inequality (Section 8) forces
+      (d) A linear-algebra ineuality (Section 8) forces
                 sum_{i != k} rank(R_ik) >= 2 d_m d_n.
       (e) Each off-diagonal R_ik is bounded by the crossing count c_ik
           between stars i and k.
@@ -1102,7 +1102,7 @@ PART X   FURTHER READING
         X_i - Y_i invertible,
         rank(R_ik) <= c_ik
          |
-         |  rank-sum inequality (Section 8)
+         |  rank-sum ineuality (Section 8)
          v
       2 d_m d_n <= 2 c(D),  hence c(D) >= d_m d_n.
          |