diff --git a/docs/src/manual/nonlinear.md b/docs/src/manual/nonlinear.md
index ae4ace22b9d..df4f63348db 100644
--- a/docs/src/manual/nonlinear.md
+++ b/docs/src/manual/nonlinear.md
@@ -353,9 +353,8 @@ op_square_2 = model[:op_square]
 
 ### Add an operator without macros
 
-The [`@operator`](@ref) macro is syntactic sugar for the
-[`add_nonlinear_operator`](@ref) method. Thus, the non-macro version of the
-preceding example is:
+The [`@operator`](@ref) macro is syntactic sugar for [`add_nonlinear_operator`](@ref).
+Thus, the non-macro version of the preceding example is:
 
 ```@repl
 using JuMP
@@ -534,7 +533,7 @@ your function which are `Float64`.
 ```julia
 function bad_f(x...)
     y = zeros(length(x))  # This constructs an array of `Float64`!
-    for i = 1:length(x)
+    for i in 1:length(x)
         y[i] = x[i]^i
     end
     return sum(y)
@@ -542,7 +541,7 @@ end
 
 function good_f(x::T...) where {T<:Real}
     y = zeros(T, length(x))  # Construct an array of type `T` instead!
-    for i = 1:length(x)
+    for i in 1:length(x)
         y[i] = x[i]^i
     end
     return sum(y)
diff --git a/src/nlp_expr.jl b/src/nlp_expr.jl
index f16e867c6bb..6fe42fcb5ee 100644
--- a/src/nlp_expr.jl
+++ b/src/nlp_expr.jl
@@ -885,8 +885,8 @@ If `dim > 1`, then the method signatures of each function must be:
  * `∇²f(H::AbstractMatrix{T}, x::T...)::Nothing where {T<:Real}`
 
 Where the gradient vector `g` and Hessian matrix `H` are filled in-place. For
-the Hessian, you must fill in the non-zero upper-triangular entries only.
-Setting an off-diagonal lower-triangular element may error.
+the Hessian, you must fill in the non-zero lower-triangular entries only.
+Setting an off-diagonal upper-triangular element may error.
 
 ## Example
 
@@ -1001,8 +1001,8 @@ If `dim > 1`, then the method signatures of each function must be:
  * `∇²f(H::AbstractMatrix{T}, x::T...)::Nothing where {T<:Real}`
 
 Where the gradient vector `g` and Hessian matrix `H` are filled in-place. For
-the Hessian, you must fill in the non-zero upper-triangular entries only.
-Setting an off-diagonal lower-triangular element may error.
+the Hessian, you must fill in the non-zero lower-triangular entries only.
+Setting an off-diagonal upper-triangular element may error.
 
 ## Example