diff --git a/poisson_dirichlet_prime_predecessors_v2.txt b/poisson_dirichlet_prime_predecessors_v2.txt
index 70b6157..86e3bad 100644
--- a/poisson_dirichlet_prime_predecessors_v2.txt
+++ b/poisson_dirichlet_prime_predecessors_v2.txt
@@ -1132,7 +1132,7 @@ The key facts needed:
     u-hit / v-hit structure.
 
 This gives the "many successes with high probability" result via
-Chebyshev's inequality. The technical input is a uniform
+Chebyshev's ineuality. The technical input is a uniform
 residue-class equidistribution of the u-hit / v-hit structure
 across groups.
 
@@ -1269,7 +1269,7 @@ We compare the AVERAGED marked sum to the UNMARKED sum:
     <= sqrt( sum_p Phi((p-1)/x) * Z_b(p-1) )
        * sqrt( sum_p Phi((p-1)/x) * |f_x(p-1) - C_x|^2 ),
 
-where the last inequality is Cauchy-Schwarz in p.
+where the last ineuality is Cauchy-Schwarz in p.
 
 The first factor is <= (C_K/b)^{1/2} * (x/L)^{1/2} by the Z_b
 bound. The second factor is <= C * (x/L)^{1/2} by the boundedness
@@ -1473,7 +1473,7 @@ sticks is small on average, as d grows.
 For a finite or summable sequence with total mass 1, sorting the
 first d coordinates gives order statistics S_{d,1} >= S_{d,2} >=
 ... >= S_{d,d}. The difference |V_i - S_{d,i}| is bounded above
-by the unmatched mass R_d (a standard rearrangement inequality).
+by the unmatched mass R_d (a standard rearrangement ineuality).
 
 So:
 
@@ -1534,7 +1534,7 @@ For every fixed nonnegative integer k, there is C_k > 0 such that:
   sum_{n <= Y} tau(n)^k         << Y (log(2Y))^{C_k},
   sum_{n <= Y} tau(n)^k / n     << (log(2Y))^{C_k}.
 
-Also main-value inequalities for Dirichlet polynomials. For
+Also main-value ineualities for Dirichlet polynomials. For
 P(t) = sum_{n <= Y} c_n n^{it}:
 
   int_I |P(t)|^2 dt         << (T + Y log(2Y)) sum |c_n|^2,
@@ -1714,7 +1714,7 @@ Chapter 19.  REFERENCES AND FURTHER READING
 
   19.3  About the analytic tools.
 
-  - H. L. Montgomery and R.C. Vaughan, "Hilbert's inequality,"
+  - H. L. Montgomery and R.C. Vaughan, "Hilbert's ineuality,"
     J. London Math. Soc. 8 (1974), 73-82. Mean-value theorems.
 
   - Trevor D. Wooley, "Vinogradov's mean value theorem via